Precision Closed-Loop Laser Pointing System for the

Precision Closed-Loop Laser Pointing

System for the Nanosatellite Optical

Downlink Experiment

Ondrej Cierny

Space Engineering, master's level (120 credits)

2017

Luleå University of Technology

Department of Computer Science, Electrical and Space Engineering

Precision Closed-Loop Laser PointingSystem for the Nanosatellite Optical

Downlink Experimentby

Ondrej Cierny

Submitted in partial fulfillment of the requirements for the degrees of

Master of Science with a Major in Space Technologyat the Luleå University of Technology

and

Master of Scienceat the Julius Maximilians University of Würzburg

on November 1st, 2017

Thesis committee

Prof. Kerri Cahoy Massachusetts Institute of TechnologyAdvisor Department of Aeronautics and Astronautics

Prof. Andreas Nüchter Julius Maximilians University of WürzburgSupervisor Computer Science VII: Robotics and Telematics

Dr. Leonard Felicetti Luleå University of Technology, Department ofExaminer Computer Science, Electrical and Space Engineering

Fabian Rein DLR Institute of Communications and NavigationExternal reviewer Department of Satellite Networks

ABSTRACT

The use of advanced small-satellite platforms has become increasingly more pop-ular in the recent years. Several private companies are investing enormous capitalinto constellations of small satellites that are designed to provide highly data-intensive global services, such as rapid Earth imaging or fast worldwide Internetaccess. The scientific community is also interested in the development of miniatureand high throughput platforms, for instance in the area of microwave radiometryor hyperspectral imaging.

The current state of the art nanosatellite radio frequency (RF) communicationssystems struggle to keep up with the increasing downlink demand and satellitedata processing capabilities. Laser communications (lasercom) offers various ad-vantages: increased bandwidth, smaller size, weight, power consumption, and alicense-free spectrum.

While the narrow beamwidths allow lasercom to achieve higher data rates thanRF, they, however, also result in higher pointing requirements for the spacecraft.Precision laser pointing systems have been successfully demonstrated on biggersatellites, but not on a nanosatellite scale, where the size and weight constraintsare so severe. The Nanosatellite Optical Downlink Experiment (NODE) devel-oped at MIT is a lasercom terminal designed to demonstrate the technologiesrequired for a high-speed optical downlink using commercial off-the-shelf com-ponents within the constraints of a typical 3U CubeSat. NODE augments the busattitude control system with a compact fine laser pointing stage to compensate forthe spacecraft body pointing error.

This thesis focuses on the development and laboratory verification of the laserpointing system for NODE. A control scheme utilizing a miniature fast steeringmirror (FSM) used to track a beacon uplink signal from the ground station is pre-sented. An on-orbit FSM calibration algorithm is developed to improve the con-trol robustness and precision. A novel sampling approach that enables closed-loopFSM control is proposed and implemented. The method focuses on simultaneoussampling of the beacon and an internal feedback signal on a single detector. Fi-

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IV ABSTRACT

nally, a hardware-in-the-loop testbed is built in the laboratory with componentsthat were selected for NODE, and the system is functionally verified and analyzedwith regards to pointing accuracy. Experimental results show that the pointing re-quirements given by the mission link budget are met, and that the system performsreliably under various laboratory-simulated conditions.

ACKNOWLEDGMENTS

First and foremost, I would like to thank my thesis advisor, Prof. Kerri Cahoy, forthe opportunity to carry out such interesting research in her laboratory, and forher constant support and advice throughout my visit. Her incredible devotion toher students and her tireless work ethic impressed me on a daily basis. I wouldalso like to thank Hyosang, Kat, Mike, Rodrigo, Rachel, and others from STAR Labwith whom I had very interesting conversations.

Next, I would like to thank many of the international students from the April J1MIT group, who I became good friends with, and who made my stay at MIT a veryenjoyable experience outside of the work environment as well.

My sincerest gratitude goes to my friends and family from Slovakia. Withoutyour encouragement and support, I would have never accomplished this work.Thank you so much.

Lastly, I would like to thank the German Academic Exchange Service (DAAD) forfunding my studies throughout the last two years through a graduate scholarship.

v

CONTENTS

Chapter 1 – Introduction 11.1 Increasing Downlink Demand in LEO . . . . . . . . . . . . . . . . . 11.2 Nanosatellite Communications Constraints . . . . . . . . . . . . . . 31.3 Laser Communications . . . . . . . . . . . . . . . . . . . . . . . . . 41.4 Thesis Objective and Structure . . . . . . . . . . . . . . . . . . . . 6

Chapter 2 – Background 72.1 Fine Pointing on Prior Missions . . . . . . . . . . . . . . . . . . . . 72.2 NODE Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.2.1 Concept of Operations . . . . . . . . . . . . . . . . . . . . . 112.2.2 Pointing Requirement . . . . . . . . . . . . . . . . . . . . . 12

2.3 Associated Research . . . . . . . . . . . . . . . . . . . . . . . . . . 13

Chapter 3 – Approach 153.1 Payload Optics Analysis . . . . . . . . . . . . . . . . . . . . . . . . 15

3.1.1 Optical Hardware . . . . . . . . . . . . . . . . . . . . . . . . 173.1.2 Signal Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.2 Pointing Control Concept . . . . . . . . . . . . . . . . . . . . . . . 263.2.1 Center of Symmetry Problem . . . . . . . . . . . . . . . . . 28

3.3 FSM Dynamics & Control . . . . . . . . . . . . . . . . . . . . . . . 293.3.1 Feedback Mapping . . . . . . . . . . . . . . . . . . . . . . . 293.3.2 Pointing Modes . . . . . . . . . . . . . . . . . . . . . . . . . 313.3.3 Dynamic Model . . . . . . . . . . . . . . . . . . . . . . . . . 333.3.4 Controller Tuning . . . . . . . . . . . . . . . . . . . . . . . . 34

3.4 Detector Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . 363.4.1 Frame Processing . . . . . . . . . . . . . . . . . . . . . . . . 36

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viii CONTENTS

3.4.2 Sampling Scheme . . . . . . . . . . . . . . . . . . . . . . . . 373.4.3 Minimizing Interference . . . . . . . . . . . . . . . . . . . . 40

3.5 Calibration Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . 413.5.1 Parameter Estimation . . . . . . . . . . . . . . . . . . . . . 413.5.2 Data Collection . . . . . . . . . . . . . . . . . . . . . . . . . 423.5.3 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . 43

3.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

Chapter 4 – Experiment 474.1 Testbed Assembly . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

4.1.1 Initial Hardware Testing . . . . . . . . . . . . . . . . . . . . 484.2 Calibration & Acquisition Testing . . . . . . . . . . . . . . . . . . . 514.3 Center of Symmetry Determination . . . . . . . . . . . . . . . . . . 534.4 Disturbance Simulation . . . . . . . . . . . . . . . . . . . . . . . . 55

4.4.1 Representative Disturbance . . . . . . . . . . . . . . . . . . 564.5 Pointing Control Verification . . . . . . . . . . . . . . . . . . . . . . 59

4.5.1 Open-Loop Test . . . . . . . . . . . . . . . . . . . . . . . . . 594.5.2 Closed-Loop Test . . . . . . . . . . . . . . . . . . . . . . . . 614.5.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

Chapter 5 – Conclusion 655.1 Thesis Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 655.2 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 665.3 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

Appendix A – Alternative Feedback Design with a Retro-Reflector 69

LIST OF FIGURES

1.1 Planet’s Dove satellite . . . . . . . . . . . . . . . . . . . . . . . . . 21.2 Opacity of the Earth’s atmosphere . . . . . . . . . . . . . . . . . . . 42.1 LCT and SOTA lasercom terminals . . . . . . . . . . . . . . . . . . 82.2 Beacon detection concept . . . . . . . . . . . . . . . . . . . . . . . 102.3 NODE concept of operations . . . . . . . . . . . . . . . . . . . . . . 113.1 Optical diagram of NODE . . . . . . . . . . . . . . . . . . . . . . . 163.2 The beacon detection hardware . . . . . . . . . . . . . . . . . . . . 183.3 Angular FOV of a lens and detector system . . . . . . . . . . . . . . 203.4 Reflectance characteristics of the DMLP1800R . . . . . . . . . . . . 213.5 Transmission characteristics of the double-bandpass filter . . . . . . 223.6 Mirrorcle Technologies FSM and Thorlabs collimator . . . . . . . . 233.7 Point spread functions of the signals . . . . . . . . . . . . . . . . . 243.8 FOV analysis of the pointing system . . . . . . . . . . . . . . . . . . 253.9 Ray geometry between the aperture and the lens . . . . . . . . . . 273.10 Illustration of an affine transformation . . . . . . . . . . . . . . . . 303.11 Open-loop pointing diagram . . . . . . . . . . . . . . . . . . . . . . 313.12 Closed-loop pointing control diagram . . . . . . . . . . . . . . . . . 323.13 Response of the dynamic FSM model . . . . . . . . . . . . . . . . . 343.14 Discrete control Simulink scheme . . . . . . . . . . . . . . . . . . . 353.15 Double-window sampling technique . . . . . . . . . . . . . . . . . 393.16 Calibration measurement patterns . . . . . . . . . . . . . . . . . . 433.17 High-level pointing chain diagram . . . . . . . . . . . . . . . . . . 464.1 Basic laboratory optical testbed . . . . . . . . . . . . . . . . . . . . 484.2 Detector sampling performance . . . . . . . . . . . . . . . . . . . . 494.3 Expanded wiring of components . . . . . . . . . . . . . . . . . . . 504.4 Calibration results with different datasets . . . . . . . . . . . . . . 524.5 Center of symmetry measurement setup . . . . . . . . . . . . . . . 534.6 Entire laboratory optical testbed . . . . . . . . . . . . . . . . . . . . 554.7 Block diagram of the whole laboratory testbed . . . . . . . . . . . . 56

ix

x CONTENTS

4.8 Calibration results with different datasets . . . . . . . . . . . . . . 584.9 Time and scatter plot of open-loop pointing error . . . . . . . . . . 604.10 Statistical analysis of open-loop pointing error . . . . . . . . . . . . 604.11 Time and scatter plot of closed-loop pointing error . . . . . . . . . 624.12 Statistical analysis of closed-loop pointing error . . . . . . . . . . . 62A.1 Ray geometry with a retro-reflector-based feedback . . . . . . . . . 69

LIST OF TABLES

1.1 Advantages and challenges of laser communications . . . . . . . . 52.1 Comparison of design parameters of selected lasercom missions . . 92.2 Downlink budgets to each ground station . . . . . . . . . . . . . . 122.3 Summary of parameters related to the pointing stage . . . . . . . . 133.1 Comparison of open-loop and closed-loop FSM control . . . . . . . 334.1 Measured detector sampling rates under varying configurations . . 494.2 Experimental results from the calibration algorithm . . . . . . . . . 514.3 Parameters used for ADCS error generation . . . . . . . . . . . . . 574.4 Accuracy metrics from an open-loop pointing test . . . . . . . . . . 614.5 Accuracy metrics from a closed-loop pointing test . . . . . . . . . . 63

xi

NOMENCLATURE

BDQ Bias-Differential Quad-channel

BER Bit error rate

COTS Commercial off-the-shelf

DAC Digital-to-analog converter

EDRS European Data Relay System

FCC Federal Communications Commission

FOV Field of view

FPA Focal plane array

FSM Fast steering mirror

FWHM Full width at half maximum

GPIO General purpose input/output

GUI Graphical user interface

ISS International Space Station

LCT Laser Communication Terminal

LEO Low Earth orbit

LPF Low-pass filter

MEMS Microelectromechanical system

MIT Massachusetts Institute of Technology

NICT National Institute of Information and Communications Technology

NIR Near-infrared spectrum

NODE Nanosatellite Optical Downlink Experiment

OCTL Optical Communication Telescope Laboratory

OGS Optical ground station

xiii

xiv CONTENTS

PDF Probability distribution function

PMC Payload microcontroller

PPM Pulse position modulation

PPP Point-to-Point Protocol

PSF Point spread function

PWM Pulse width modulation

RF Radio frequency

RMS Root mean square

SNR Signal-to-noise ratio

SOTA Small Optical TrAnsponder

SPI Serial Peripheral Interface

SSO Sun-synchronous orbit

STAR Lab Space Telecommunications, Astronomy, and Radiation Laboratory

SWaP Size, weight and power consumption

TROPICS Time-Resolved Observations of Precipitation structure and storm In-tensity with a Constellation of Smallsats

UART Universal asynchronous receiver-transmitter

USB Universal Serial Bus

WDM Wavelength division multiplexer

CHAPTER 1

Introduction

The use of small satellites has seen a vast increase in popularity in the recent years.Ride-sharing with bigger satellites has allowed much cheaper launch opportunitiesfor smaller payloads as secondary cargo and opened the low Earth orbit (LEO)to more potential customers. Autonomous deploying mechanisms, such as theNanoRacks CubeSat Deployer on the International Space Station (ISS) or otherspecialized launcher adapters greatly facilitate the deployment of tens to hundredsof small satellites on a single launch, allowing customers to split the expense andaccess more frequent launch spots [1].

1.1 Increasing Downlink Demand in LEO

With easier access to space and quick pace of technological improvement, thesatellite builders pursue faster, iterative development cycles. This paves the wayfor more advanced and miniaturized technologies into their payloads with increas-ing processing power and data acquisition capacity. There are multiple exampleswhich illustrate how immensely data-intensive LEO applications of small satellitescan be with currently available technology.

In the category of scientific missions, a constellation currently being designedat the MIT Lincoln Laboratory, called TROPICS, aims to use CubeSats to providerapidly updated data for weather models. The twelve planned satellites will con-tinually scan the swath of atmosphere below using microwave radiometers andproduce data at a steady rate of about 16 kbps, thus, generating about 1.5 GB ofinformation to be downlinked per satellite per day [2].

Another even more data-intensive application of high scientific interest is hy-perspectral imaging, where the inclusion of additional frequency channels in thecollected imagery substantially increases the output data rate. A disaster moni-toring mission depicted by Tsitas and Kingston proposes a multispectral CubeSat

1

2 INTRODUCTION

imager for tracking the progress of a flood, generating 127 Mb of compressed dataevery second of operation [3]. A mission outlined by Mandl et al. equips a Cube-Sat with an even more sophisticated hyperspectral imager that would produce rawdata rates on the order of Gbps, collecting over a terabyte of information over oneorbit, assuming enough power is available for continuous operation [4].

In the category of commercial missions, several private companies are currentlydeveloping constellations of small satellites designed to provide various attrac-tive global services, focused mainly on remote Earth sensing and worldwide low-latency Internet connectivity.

Planet (formerly Planet Labs), a startup focused on rapid Earth imaging, hasalready launched over a hundred CubeSats weighing below 5 kilograms, andequipped with 3-5 meter resolution imaging capabilities. The satellites, calledDoves (see Figure 1.1), contain an optical telescope that occupies most of thespace in its 3U bus [5]. Each Dove takes a roughly 4 MB sized image every sec-ond, and together, the constellation acts as a line scanner for the whole Earth. Inits full capacity, Planet plans to operate up to 150 satellites in a Sun-synchronousorbit (SSO) and provide access to sub-daily new imagery of the entire planet. Toaccomplish this goal, it must downlink approximately 6 TB of images every day.As of 2016, the company was capable of downlinking 550 GB of imagery per dayover its X-band downlinks, with a data rate of up to 84 Mbps [6].

Figure 1.1: A Dove - Planet’s rapid-imaging CubeSat [7].

Other, more enormous commercial constellations are being developed with thegoal of providing worldwide low-latency Internet connectivity from LEO. One ofsuch proposals came from OneWeb, a company which recently successfully ob-tained a license from the Federal Communications Commission (FCC) to operateits constellation of 720 small satellites [8]. With an outlined capacity of ten ter-

1.2. NANOSATELLITE COMMUNICATIONS CONSTRAINTS 3

abits per second, it is also a good example of how the data throughput from smallsatellites is rapidly increasing.

1.2 Nanosatellite Communications Constraints

As the number of small satellites in orbit grows and their downlink demand isgetting higher, pressure is put on their on-board communications systems andthe ground-based receiver infrastructure. There are, however, fundamental con-straints in increasing the downlink rates from nanosatellites using currently avail-able technology.

The primary engineering constraint of a small satellite platform is its size, weightand power consumption (SWaP). SWaP is fundamental to on-board communica-tions systems, as more power and size generally means higher performance com-munications capability. As the link capacity inherently depends on the channelbandwidth and the signal-to-noise ratio (SNR), the higher the received power is,the higher the chance is to achieve fast downlink rates.

We can analyze the constraints further by looking at the simplified version of thelink equation, also called the Friis transmission formula:

PRx ∝PTxATxARx

λ2R2(1.1)

where PRx is the received power, PTx is the transmitted power, ATx is the trans-mitter aperture area, ARx is the receiver aperture area, λ is the wavelength and Ris the distance between the receiver and the transmitter.

It can be seen that most of the terms in play are difficult candidates for radicalimprovement, either due to SWaP or cost constraints. PTx is fundamentally limitedby the available power on the satellite (e.g. photovoltaic technology). ATx is con-strained by the size and mass of the satellite, while a high ARx antenna would bevery costly for a nanosatellite operator. R is given by the orbit, and so is essentiallyconstrained by physics. The only term where order-of-magnitude improvementsare technologically feasible is the wavelength/frequency.

Historically, the majority of CubeSat-sized missions have flown with lower fre-quency (UHF or S-band) communications systems, with data rates of up to 3Mbps [9]. A few organizations are developing transceivers in the higher frequencyX and Ka-bands. As mentioned, Planet is flying X-band transmitters and has regis-tered spectrum for theoretical downlinks of up to 200 Mbps [9]. Syrlinks has alsodeveloped commercially available X-band radios for CubeSats [10, 11]. However,the licensing of the high-frequency RF spectrum that is necessary for faster down-links is a huge bottleneck. Especially for projects with a limited budget and a fastdevelopment cycle, obtaining a portion of the spectrum in the higher bands is ex-tremely difficult and can take longer than the time needed to design, manufacture

4 INTRODUCTION

and test the whole satellite [12,13]. In general, the situation in the overcrowdedRF spectrum is expected to worsen as more satellites enter into orbit and licensingorganizations such as the FCC struggle to keep up with the demand [14].

In conclusion, the small satellite platform lacks a convenient and scalable high-rate communications solution.

1.3 Laser Communications

Lasercom is one of the key contenders in providing next generation high-rate spacecommunication links. It utilizes laser beam propagation in free space as the sig-nal carrier, often in the visible or near-infrared (NIR) spectrum. This makes laserdownlinks and uplinks feasible, as the Earth’s atmosphere is sufficiently transpar-ent at these wavelengths, similarly as in the radio “window” (Figure 1.2).

Figure 1.2: Opacity of the Earth’s atmosphere to electromagnetic radiation [15].

The orders-of-magnitude shorter wavelength is the core benefit of lasercom, be-cause it enables narrower beams given the same effective aperture size. With anarrower beam, the energy density of the signal increases, which leads to more

1.3. LASER COMMUNICATIONS 5

efficient SWaP utilization. The spectrum is also attractive because of the enormousbandwidth that it encompasses. In fact, the entire bandwidth of the RF spectrumcan fit within a small window of the NIR spectrum portion that is utilized forlasercom. Since the carrier frequencies are on the order of terahertz, there is anextensive amount of bandwidth available. The second significant benefit is thatthis spectrum is nearly unregulated. Since the narrow beamwidths present negli-gible risk of interference, the only regulations on lasercom in general are imposedwith regards to eye safety [16]. For lasercom downlinks, however, the transmittedpower is spread out over a larger area, and thus is far below the maximum permit-ted exposure limit. Safety has to be, however, considered for the case of uplinkssince the power is concentrated on the ground.

With the narrow beamwidths, however, lasercom becomes challenging to im-plement due to the accurate pointing that needs to be established between thetransmitter and the receiver. Depending on the beamwidth (divergence) used, therequired pointing accuracy is usually beyond the satellite’s body pointing capabil-ity, and so fine pointing stages have to be implemented [17]. This is especiallychallenging for nanosatellites, given the strict SWaP constraints.

Another obvious issue of lasercom is its susceptibility to atmospheric effects.Cloud coverage can lead to absorption, or even complete obstruction of the down-link line of sight. Atmospheric turbulence also leads to undesired variations insignal intensity, phase, and direction [18]. These effects are primarily mitigatedby site selection and ground station diversity [19,20]. Studies have shown that acombination of three or more sites can lead to a downlink availability higher than90% [21].

Table 1.1: Summary of key advantages and challenges in the implementation of lasercom.

Advantages+ Better SWaP utilization: higher gain with smaller terminals+ Highly directional: interference or interception is unlikely+ Regulatory benefits: free spectrum and essentially unlimited bandwidthChallenges– Precision pointing required– Atmospheric channel impairments– Eye safety regulations for uplink

Ultimately, if the outlined challenges can be solved, the benefits of lasercom canbe extremely advantageous, especially for small satellite platforms. The ability todownlink more data with less SWaP, and the advantage of free spectrum alloca-

6 INTRODUCTION

tion, can enable a wide variety of new interesting scientific as well as commercialmissions, that are either impossible or very difficult to implement with currentlyavailable nanosatellite communications technology.

1.4 Thesis Objective and Structure

To demonstrate the feasibility and benefits of using lasercom on a nanosatelliteplatform, the MIT Space Telecommunications, Astronomy, and Radiation Labora-tory (STAR Lab) is currently developing a CubeSat communications payload calledthe Nanosatellite Optical Downlink Experiment (NODE). NODE targets a 10-100Mbps optical downlink, with the primary aim of demonstrating a variety of tech-nologies that are necessary to enable scalable high-rate lasercom within a highlySWaP constrained environment. One of the technologies is a compact fine laserpointing stage that augments the host satellite’s body attitude determination andcontrol system (ADCS).

This thesis focuses on the fine pointing system of NODE. Although NODE, in-cluding its pointing subsystem, is essentially past the design review, there is nointegrated hardware setup of the subsystem developed yet. While some com-ponents of the system were individually tested, a general hardware-in-the-looptestbed of the pointing system is needed to develop and verify the fine pointingalgorithms. Thus, the primary goal of this work is to advance the technology readi-ness level of the system by developing such setup, with emphasis on the followingsub-objectives:

1. Assemble the optics and electronics of the fine pointing system based on theNODE design in the laboratory.

2. Develop embedded pointing control algorithms for the system hardware.

3. Research how the inclusion of an internal calibration laser can improve thepointing accuracy and robustness.

4. Verify the precision of the fine pointing system under the expected host satel-lite body pointing disturbance.

The thesis is structured into five major chapters. The next chapter focuses on fur-ther research background on the topic and on the NODE system-level architecture.Chapter 3 covers all theoretical aspects of the development process (i.e. mainlysub-objectives 2 and 3). Chapter 4 focuses exclusively on the practical and exper-imental aspects of the work (objectives 1 and 4). The last chapter summarizes theachieved results, the thesis contributions, and discusses future work.

CHAPTER 2

Background

In this chapter, we investigate prior successful demonstrations of fine laser point-ing on satellites, and compare their approach with the challenges associated witha nanosatellite implementation. Afterwards, we present the NODE system-levelarchitecture and derive the fine stage pointing precision requirement. Lastly, arecapitulation of previous research that has been carried out in STAR Lab withregards to the fine pointing system is given, with emphasis on takeaways that arelinked to the objectives of this thesis.

2.1 Fine Pointing on Prior Missions

In the recent years, a large number of different lasercom links have been demon-strated, in scenarios including LEO-to-ground [22, 23], LEO-to-LEO [24], GEO-to-ground [25, 26], GEO-to-LEO [27, 28], deep space-to-ground [29], ground-to-deep space [30], GEO-to-aircraft [31], aircraft-to-ground [32, 33], aircraft-to-aircraft [34], and stratospheric balloon-to-balloon [35]. Several interestingprojects are also in development for demonstration in the near future [36–42].

The vast majority of the successful missions utilize some kind of fine pointingmechanism to improve the beam pointing accuracy. While most of the missions areoutside the scope of NODE in terms of targeted usage area or SWaP, two systemswith comparable utilization and parameters are highlighted here for analysis.

The first notable system is the Laser Communication Terminal (LCT), developedby the German company Tesat Spacecom. LCT is a more generic design that wassuccessfully used on multiple missions. The first generation of LCT was launchedin 2001 to demonstrate lasercom links between LEO and GEO, but also successfullycompleted a LEO downlink measurement campaign [43]. Recently, the secondgeneration of LCT was implemented, as part of the European Data Relay System

7

8 BACKGROUND

(EDRS) mission. EDRS is a constellation of GEO satellites designed to relay databetween LEO satellites and ground stations that would be otherwise outside thesatellite’s line of sight. Under EDRS, LCT successfully demonstrated 1.8 Gbps linksbetween Sentinel-1 in LEO an Alphasat in GEO in 2014 [44].

The LCT pointing system consists of 4 independent pointing stages on top of thehost spacecraft body pointing capability. This includes a two-axis gimbal assembly,a coarse FSM, a fine FSM, and ultimately a mirror dedicated for point-ahead anglecompensation on the downlink [45]. LCT is by design a bidirectional system,so the transmitted signals also provide pointing feedback to the receiver sides.Altogether, the coarse gimbal assembly and the three steerable mirrors enable aRMS pointing accuracy of 100 µrad [43]. LCT weighs 56 kilograms and duringpeak transmission consumes 160 W of power, and so is deployable only on mediumto large satellite platforms.

The second notable system is the Small Optical TrAnsponder (SOTA), devel-oped by Japan’s National Institute of Information and Communications Technol-ogy (NICT). SOTA is a lasercom terminal designed to fit on a host microsatellitebus called SOCRATES. SOTA augments the bus ADCS with two pointing stages: agimbal assembly and an FSM. It incorporates four different downlink lasers, twoof which are used for communications at different wavelengths [46].

Figure 2.1: On the left, the LCT, made by Tesat Spacecom, with an aperture diameter of 13.5cm [47]. On the right, the NICT-designed SOTA, as part of the SOCRATES spacecraft, withan aperture diameter of only 5 cm (images are not drawn to scale) [48].

SOTA utilizes a beacon uplink laser from the ground station for precision point-ing feedback, and while it is locked, achieves a pointing accuracy of about 150

2.1. FINE POINTING ON PRIOR MISSIONS 9

µrad, based on measurements of pointing losses [49]. The lasercom terminalweighs only 5.9 kg and consumes 40 W of power. Since it launched in 2014, SOTAsuccessfully demonstrated several lasercom downlinks from LEO at 10 Mbps.

While SOTA has been one of the most compact lasercom satellite terminalsdemonstrated so far, its SWaP is still beyond what nanosatellite platforms canoffer. A typical 3U CubeSat weighs no more than 4 kilograms and typically con-sumes only 10 to 20 W. In order to address the satellite platforms of this scale,further miniaturization and SWaP reduction of the terminals is necessary, and thusheavy mechanisms such as gimbals have to be inevitably avoided. In Table 2.1,the key design parameters of LCT and SOTA are summarized, and compared withthe targeted parameters of NODE.

Table 2.1: Key design parameters of LCT and SOTA vs. targeted NODE parameters.

Design parameter LCT 2nd Gen. SOTA NODELink type LEO-GEO-ground LEO-ground LEO-groundWavelength (nm) 1064 976/1550 1550Data rate 1.8 Gbps 1/10 Mbps 10-100 MbpsRange (km) < 45000 < 1000 < 1000Mass (kg) 56 5.9 0.6Transmitted power1 (W) 2.2 0.27/0.04 0.2Power consumption (W) 160 40 15Aperture diameter (cm) 13.5 5 2.54# of pointing stages2 5 3 2Pointing accuracy3 (µrad) 100 ~150 < 100 (exp.)

1Average transmitted power values.2This number includes the host spacecraft ADCS.3Root mean square (RMS) pointing accuracy.

10 BACKGROUND

2.2 NODE Architecture

NODE aims to advance the state of the art in nanosatellite communications andprovide a high-bandwidth downlink that is compatible with the SWaP constraintsof a typical CubeSat. It is designed to occupy approximately 1U, and so serve asa potential communications payload for different host CubeSats. The first gener-ation has a baseline goal of a 10 Mbps link rate and a stretch goal of 100 Mbps.It was, however, designed to be scalable, and so much higher data rates are en-visioned in the next generation, once the fundamental technology and design issuccessfully demonstrated in flight.

To increase the affordability and performance, commercial off-the-shelf (COTS)components are used in the design where feasible. This also led to the choice ofthe downlink wavelength of 1550 nm, as its wide usage in the fiber optics industrycaused wide availability of COTS components, such as optical fiber amplifiers [50].Apart from the downlink 1550 nm laser, the NODE design also utilizes an uplinkbeacon laser to facilitate precise pointing. The beacon is transmitted from theoptical ground station (OGS) and detected on an on-board detector, so that thefine pointing stage has accurate knowledge of the OGS location, and can track itby steering an FSM. The host satellite also contains a regular bi-directional radioto be used for telemetry transmission.

Figure 2.2: Illustration of beacon detection on-board NODE [51].

2.2. NODE ARCHITECTURE 11

2.2.1 Concept of Operations

The operational concept of NODE can be split into three major phases. In thefirst phase, the whole satellite will begin a slew maneuver to point towards theOGS using the bus ADCS. This ensures that the OGS will be within the beacondetection system field of view (FOV) at all time. In the next phase, the OGS willbegin to track the satellite as it as passes over, and transmit the beacon navigationsignal. Once the beacon is acquired on the NODE detector, the fine pointing stagewill begin the third, tracking phase, during which it will lock onto the signal andinitiate the laser downlink.

Figure 2.3: The three operational phases required to initiate a lasercom downlink. In the firstphase the whole satellite body slews towards the OGS, so that the uplink beacon is within thedetector’s FOV. After the beacon is acquired, the fine pointing stage is initiated, and will trackthe beacon signal with high precision. Finally, the laser downlink is initiated [52].

The primary targeted OGS for the downlink demonstration is the Optical Com-munication Telescope Laboratory (OCTL) operated by the NASA Jet PropulsionLaboratory, located at the Table Mountain Observatory in California. OCTL has aone meter receiver aperture, which will facilitate downlinks up to an expected rateof 100 Mbps. OCTL also includes a powerful 9 W beacon laser with a wavelengthof 976 nm, for which the NODE beacon detection system was designed.

Simultaneously with NODE, STAR Lab is also developing an amateur portableoptical ground station of its own to be used as a compact receiver. The portableOGS is based on an amateur telescope for astronomy, albeit extended with a cus-tom opto-electronic module to enable processing of the downlink signal. The

12 BACKGROUND

telescope has an aperture size of �30 cm, and 10-50 Mbps rates are expectedwhen it will be used for communications. The downlink budget to each OGS issummarized in Table 2.2 and analyzed in greater detail in [36].

Table 2.2: Simulated link budget to the portable OGS and to OCTL at JPL [36].

Parameter Portable OGS JPL OCTL Units

Channel data rate 9.9 43 MbpsPPM order 128 16

Average optical power -7.0 -7.0 dBWTransmit optical loss -1.5 -1.5 dBTransmit gain 65.0 65.0 dBiPointing loss -3 -3 dBPath loss (1000 km) -258.2 -258.2 dBAtmospheric loss -1.0 -1.0 dBReceive gain 114.7 126.1 dBReceive optics loss -2.0 -3.0 dBReceive implementation loss -3.0 -3.0 dBSignal power at detector -92.9 -82.6 dBWNeeded power for BER = 10−4 -93.2 -84.2 dBW

Margin at 1000 km 0.23 1.62 dBMargin at 600 km 3.04 4.30 dB

2.2.2 Pointing Requirement

NODE is designed with a single FSM-based fine pointing stage, which has to beversatile enough to reject the whole possible range of the spacecraft body point-ing error. To reach its mission goal, the beamwidth of the NODE transmitter waschosen based on the downlink budget analysis and the availability of COTS colli-mators [50,53]. As a result, a beam collimator with a full width at half maximum4

(FWHM) divergence angle of 1.3 mrad was selected.Since the downlink plan budgets a maximum of 3 dB for pointing losses, the

beam has to be steered within its FWHM angle, so that at least the half-maximumpower hits the receiver. This sets the pointing accuracy requirement of the finepointing stage to ±0.65 mrad. The minimum range within which the system hasto operate was chosen in the early NODE design phase based on the expected

4Also referred to as the half-power beamwidth in traditional RF communications.

2.3. ASSOCIATED RESEARCH 13

worst-case host satellite pointing capability. To make the design compatible withstandard CubeSat pointing capabilities a minimum pointing range of ± 3 deg wasderived [53].

Table 2.3: Summary of parameters and requirements related to the pointing stage.

Divergence angle (FWHM) 1.3 mradPointing requirement (-3 dB) ± 0.65 mradMinimum fine pointing range ± 3 deg / ± 52.4 mrad

2.3 Associated Research

In this section, we summarize previous research that was done in STAR Lab andis related to the NODE pointing system. Relevant prior takeaways that influencedthe development of this thesis are also highlighted.

Pointing, Acquisition, and Tracking Analysis

T. Nguyen and K. Riesing built on top of the initial work of R. Kingsbury, andstarted the design from which the current fine pointing system is derived [50,52, 53]. [52] thoroughly researched the beacon detection approach, and selectedthe hardware candidates for the beacon detector and the focusing lens. It alsoinvestigated potential frame processing algorithms for hardware implementation,which inspired some parts of the development process in this thesis, especially inthe area of reliable beacon acquisition and tracking.

Characterization of the FSM that was selected for NODE was also researchedin [50,53]. By identifying various small sources of error in the open-loop steeringof the mirror, including thermal deformation, zero position shift, sensitivity, andrepeatability, the research inspired the potential of rejecting these errors by inclu-sion of a calibration laser in the newest design, which is a core research area ofthis thesis.

Beacon Link Budget

The work in [51,52] also focused on the design of a beacon link budget based onthe selected NODE hardware and parameters of the OCTL beacon laser. The re-sulting simulation was further adapted by R. Morgan, and provides good analysis

14 BACKGROUND

of the expected power on the beacon detector, which helped during the design ofthe acquisition and tracking algorithms in this thesis [54].

Optomechanical Alignment Analysis

Another area of research from which this work benefited is an optomechanicalalignment analysis of the current NODE optical design performed by M. Lee [55].As part of the analysis, a simulation of the selected NODE optics was implementedin the Zemax environment, which helped understand various optical properties ofthe system, such as the focused laser spot sizes, point spread functions, and raygeometries.

CHAPTER 3

Approach

To point precisely at the receiver, NODE relies on a fine laser pointing systembased on a beacon detector and an FSM, which augments the ADCS of the space-craft bus and corrects for its pointing error. In Section 3.1, the NODE optics andthe pointing system structure is described in detail, with some remarks on theselected flight hardware. Afterwards, the system is analyzed from a control engi-neering standpoint. In Section 3.3, the FSM dynamics are further analyzed, andan approach on the design of a closed-loop controller is presented. Section 3.4focuses on the beacon acquisition and laser tracking algorithms, while Section 3.5describes the derivation of a calibration algorithm devised to improve the controlprecision and robustness. Finally, Section 3.6 gives a high-level summary of thedesigned embedded control chain as a whole.

3.1 Payload Optics Analysis

A diagram depicting the core architecture of the NODE optics is shown in Figure3.1. From a communications point of view, the architecture follows a monostaticdesign, as it only has a single aperture, through which the transmitted laser aswell as the received beacon signal travels.

The beacon signal (light blue in Figure 3.1) is detected on-board the satellite ona camera through a focusing lens assembly. The downlink signal (red) is amplifiedin a fiber, collimated, and then reflected from the FSM and a dichroic1 mirroroutwards from the satellite. The fine pointing control is done by steering the FSMbased on the angle of incidence of the beacon beam.

One disadvantage of the MEMS FSMs is that they lack any feedback sensors. This

1Dichroic mirrors are characterized by having different reflectance/transmission properties fordifferent wavelengths of light.

15

16 APPROACH

Figure 3.1: Optical diagram of NODE.

fact, combined with the possible misalignments in the system due to thermal andother effects can result in poor knowledge of where exactly the downlink signal isbeing pointed. For this reason, an internal calibration laser (black on diagram) wasalso included in the system design, albeit with a different wavelength, such thatit is not reflected outwards from the satellite but back into the on-board camera.Sampling this signal on the camera then provides a direct optical feedback ofwhere the FSM is pointing.

As outlined in Section 2.2, NODE leverages different wavelengths for different

3.1. PAYLOAD OPTICS ANALYSIS 17

purposes. All in all, the signals can be summarized as follows:

• Beacon signal: 976 nm laser beam from the ground station provides on-board knowledge of the ground station’s location.

• Downlink signal: 1550 nm modulated downlink beam is used to transmitdata to the optical ground receiver.

• Internal calibration/feedback signal2: 635 nm internal calibration laser isused as optical feedback of the FSM pointing angle.

3.1.1 Optical Hardware

In this section, a summary of the most important components used mainly as partof the fine pointing system is presented. As is common with CubeSat hardware,NODE too relies on COTS parts where feasible, which holds true for all the opticalcomponents. For the most part, the hardware was selected after numerous designiterations and trade-off studies, which, if relevant, are referred to in each casetogether with brief reasoning on the final component selection.

Internal Laser Sources

NODE internally generates two optical signals: the downlink signal and the cali-bration signal. The 1550 nm transmitter design is not covered in this thesis as itis not essentially relevant to the pointing system. Its design is based on previousresearch done by R. Kingsbury which is presented in great detail in [50].

The calibration laser itself does not need to be modulated as it is merely usedas an optical feedback of the internal pointing angle, and thus a simple fiber-coupled laser diode that can be switched on and off is sufficient. Its most importantproperty of interest is the output power. Since the beacon camera is meant todetect very low power light from the uplink beacon due to its significant free-spacepath loss, the calibration laser should ideally be as low power as possible becausethe beam experiences negligible losses internally with comparison to the beaconsignal (tens of dB vs. hundreds) [52]. The diode that was ultimately selected is a1 mW fiber-coupled 635 nm laser diode manufactured by QPhotonics.

Beacon Detector

One of the most important pieces of hardware for beacon detection and trackingis the on-board camera. K. Riesing and T. Nguyen examined several focal plane

2Throughout this text this is referred to as either the calibration or the feedback signal/laser.

18 APPROACH

arrays (FPAs) in [51, 53] and assessed which would best suit NODE. The beaconwavelength, being not too far in the infrared spectrum, allows for utilization ofsilicon detectors. These are significantly more affordable than sensors that operatewholly in the infrared, like InGaAs-based or similar. The main factors consideredin the selection of the FPA were readout noise, dark current, quantum efficiencyin near-IR, the pixel pitch and former space heritage.

After multiple design iterations, the 5-megapixel Aptina MT9P031 FPA was se-lected due to its small pixel size of 2.2 µm and previous space heritage. The smallpixel pitch allows for using shorter focal length lenses (hence saving space) whileretaining good angular resolution for beacon tracking. The sensor has a quantumefficiency of 3% at 976 nm, which is sufficient for detection of the OCTL beacon.A compact COTS industrially packaged camera which incorporates the Aptina FPAand control electronics in a housing was selected from the German manufacturerMatrix Vision. The whole package is only 40 mm wide and weighs about 80 grams(see Figure 3.2).

Figure 3.2: On the left, the Matrix Vision mvBlueFox-IGC [56]. On the right, the SchneiderOptics Xenoplan 1.4/23 Compact lens assembly [57].

Focusing Lens

Under ideal conditions, the lens system focuses the inbound beacon beam into apoint on the detector whose location determines the angle of the beam’s incidence.T. Nguyen created a list of COTS lens assemblies for NODE that are potentiallysuitable for flight and are vacuum-compatible in [52]. The primary property ofinterest of the lens is the focal length which determines the detector’s field of view


(FOV). Apart from the FOV, low aberrations and a compact size were the drivingfactors in the selection process.

To correct for lens aberrations and ensure beacon detectability across the FOV, asystem with multiple elements is preferred, as it performs better in maintaining ahigh brightest pixel flux fraction at different field angles [52]. Larger lens aperturealso improves detectability by collecting more photons and thus increasing the re-ceive chain gain. Ultimately, the selection came down to a compact lens assemblyby Schneider Optics from the Xenoplan series (Figure 3.2). The Xenoplan 1.4/23is a compact 6-segment lens assembly with a focal length of 22.5 mm and a clearaperture of approximately �16 mm. The manufacturer also offers a ruggedizedversion of the lens which offers stable imaging performance even in shock and vi-bration dominant environments, which is of great benefit due to the harsh satellitelaunch conditions.

Knowing the detector and lens properties, two important parameters of the bea-con tracking system can be calculated: the total angular FOV of the system and theFOV of one pixel on the sensor. As can be seen in Figure 3.3, using the similarityof triangles, the half-angle angular FOV of the setup can be defined as:

AFOV

2= tan−1

(h

2f

)(3.1)

where h is either the detector’s height or width and f is the focal length of the lens.Substituting in the hardware properties, the sensor’s half-angle FOV is calculatedto be 5.43 degrees vertically and 7.22 degrees horizontally. Similarly, substitutingh2

with the pixel size, the pixel angular FOV is found to be 0.0056 degrees, or ap-proximately 98 µrad. A more comprehensive FOV analysis is presented in Section3.1.2 - Signal Analysis.

Dichroic Mirror

The dichroic mirror is located between the focusing lens and the satellite’s mainaperture. It is an important component from an optics standpoint as it determinesthe routing of the optical signals depending on their wavelength. Its intendedpurpose can be summarized in three points:

1. Reflect as much of the downlink 1550 nm signal as possible outwards throughthe main satellite aperture, i.e. act as a mirror.

2. Partially pass and partially reflect the 635 nm feedback signal, such that itcan be detected on the camera, i.e. act as a beamsplitter.

3. Ideally, do not reflect any of the 976 nm signal so beacon detectability is notworsened, i.e. act as a window.

20 APPROACH

Figure 3.3: Angular FOV of a lens and detector system.

The dichroic mirror is placed at 45 degrees relative to the aperture’s optical axis. Aregular mirror is added on its side in order to reflect the partially passed feedbacksignal back and then to the camera through the focusing lens.

Due to the very specific requirements, finding an affordable COTS component ofsuch properties is not easy. Eventually a trade-off was made and a COTS dichroicmirror manufactured by Thorlabs was selected, instead of ordering a custom so-lution. The Thorlabs DMLP1800R is a rectangular longpass dichroic mirror witha cutoff wavelength of 1800 nm. The primary property of interest is the mirror’sreflection band between 1500 - 1750 nm which is guaranteed to be above 90% bythe manufacturer. The bands for 635 nm and 976 nm are outside the mirror’s in-tended operating range and are determined mainly by the manufacturing process.The reflectance characteristics of DMLP1800R can be seen in Figure 3.4 below,with the bands of interest highlighted in red.

It can be seen that the DMLP1800R mostly fulfills the needed criteria. The 1550nm signal is almost perfectly reflected, with 99% reflection at this wavelength.The dichroic mirror reflects 85% of 635 nm light, therefore, assuming no loss,15% is transmitted through, and 85% of that is then reflected towards the cameraafter reflection from the side mirror. Consequently, taking into account potentiallosses on both the dichroic and the regular mirror, about 10% of power from thecalibration laser diode reaches the focusing lens, which is sufficient as the signalis generated internally and experiences negligible free-space path loss. The onlydrawback of DMLP1800R is the higher 53% reflectance at 976 nm, which had tobe taken into account during the beacon link budget analysis.


600 800 1000 1200 1400 1600

Wavelength, (nm)

0

20

40

60

80

100

Re

fle

cta

nce

, R

(%

)

DMLP1800 Reflectance

Figure 3.4: Reflectance characteristics of the DMLP1800R, with bands of interest highlightedin red. The data is for unpolarized light with a 45 degree angle of incidence [58].

Bandpass Filter

To minimize noise on the beacon detector and thus add margin to the beacon linkbudget in terms of SNR, a bandpass filter is added to the satellite’s main apertureto block background light from the Earth. The filter also helps protect the lens as-sembly from potentially damaging UV radiation from the Sun. A double-bandpassdesign was selected to attenuate all wavelengths apart from the downlink 1550nm and the 976 nm beacon signal from the OGS. In this case, a ready-availableCOTS solution is unavailable, instead, a custom filter was ordered from the sup-plier Omega Optical. The characteristics of the received filter are shown in thegraph in Figure 3.5.

The transmission at the center wavelengths of 1550 and 976 nm is above 85%with passband bandwidths of about 80 nm and 40 nm respectively. Out of thesebands the transmission is on average below 0.02% which corresponds to about-37 dB of attenuation. The benefits of this in terms of SNR were addressed in thebeacon link budget developed by T. Nguyen and R. Morgan (Section 2.3).

FSM

The FSM is integral to the fine pointing system: it steers the downlink beam to-wards the OGS based on the beacon’s angle of incidence. Technological advance-ments in the industry that led to the development of ultra-compact microelec-tromechanical (MEMS) FSMs were one of the key enablers that made the NODEdesign feasible given the highly space and weight constrained environment.

22 APPROACH

800 1000 1200 1400 1600 1800

Wavelength, (nm)

0

20

40

60

80

100

Tra

nsm

issio

n,

T (

%)

Double-bandpass Transmission

Figure 3.5: Transmission characteristics of the custom Omega Optical double-bandpass filter.

The fine pointing system utilizes a MEMS FSM manufactured by Mirrorcle Tech-nologies. The company offers a variety of 2-axis FSMs based on mirror size andsteering range that are built in an extremely compact chip-scale package. ForNODE, the most compact version that is pre-soldered on a small printed circuitboard was selected, with a mirror diameter of �3.6 mm and a mechanical steer-ing range of ±3 degrees (the reasoning for the chosen range is given in Section3.1.2 - Signal Analysis). The entire package, called TINY20.3, is only 20 x 13 mmin size (see Figure 3.6). The FSM dynamics are further discussed in Section 3.3 -FSM Dynamics & Control.

Collimator

The collimator is turning the fiber-propagated optical signal into a collimated free-space beam. Its properties determine the beam divergence angle, which in turn de-termines the pointing requirements. As described in Section 2.2.2, the beamwidthwas chosen based on the link budget, as well as the availability of COTS compo-nents. A collimator from Thorlabs with a FWHM divergence angle of 1.3 mradwas eventually chosen. The CFS5-1550-APC is factory-calibrated for 1550 nmlight, has a diameter of �1 mm and is about 2 mm in length (see Figure 3.6).

Coupler

To ensure that the downlink signal and the calibration signal share the same exactbeam path to the FSM, they need to be coupled into one fiber and fed into thesame collimator. For this reason, a wavelength division multiplexer (WDM) is


Figure 3.6: On the left, the Mirrorcle Technologies FSM in a TINY20.3 TinyPCB package [59].On the right, the Thorlabs CFS5-1550-APC Pigtailed Aspheric Collimator [60].

used. A WDM by Thorlabs (WD202A) was selected for NODE as the best COTSalternative. The WDM is intended to combine 1550 and 980 nm signals, but thevendor confirmed that the 980 nm channel can be used with a 635 nm signal withslightly higher insertion loss as the only drawback.

3.1.2 Signal Analysis

To further analyze the influence of the optical components on each signal, a sum-mary of the signal paths with some relevant nuances that were identified is pre-sented, together with a comprehensive depiction of the system’s FOV (Figure 3.8)and the expected signal point spread functions (PSFs) on the FPA (Figure 3.7).

Beacon to Camera Path

The beacon signal is generated in the vicinity of the optical ground station to pro-vide the most accurate knowledge of the receiver’s location. The collimated 976nm beam experiences significant power losses due to its divergence, atmosphericconditions and the beacon detection optics. The link parameters are analyzed indepth by T. Nguyen and R. Morgan in [52,54]. The expected SNR on the detectorranges from 14 to approximately 17 dB, which facilitates reliable detection. Sincethe beacon beam will be well collimated, the spot size on the detector is expectedto be very small. An optomechanical simulation model developed by M. Lee re-vealed that the expected beacon spot size on the detector is around �10 micronswhich translates to ca. 5 pixels across [55]. As there are no obstructions to thebeacon beam, under favorable conditions, its spot is detectable across the entirecamera full-angle FOV of 14.44 x 10.86 degrees (double the calculated half-angleFOV in Equation 3.1).

24 APPROACH

Calibration Path

The calibration laser diode produces a 1 mW fiber-coupled signal that is fed into aWDM for coupling with the downlink signal and then transmitted into free spacefrom the collimator. It has to be taken into consideration that the selected col-limator is tuned for the wavelength of the transmission signal and will performsub-optimally for the wavelength of the calibration laser. This is mainly due tochromatic aberration of the collimation lens, which makes its effective focal lengthdepend on the input wavelength. Consequently, the calibration beam will not beperfectly collimated and the spot size will be bigger on the FPA. Similarly as for thebeacon path, the simulation model revealed that this size should be approximately�120 microns, or ca. 55 pixels across [55]. The model did not, however, accountfor a focusing lens corrected for chromatic aberrations (such as the Schneider Op-tics lens), and such this value is expected to be smaller in the real system. ThePSFs of both the calibration and the beacon signal calculated in the simulation areshown in Figure 3.7 below.

Figure 3.7: PSF of the beacon (left) and the calibration (right) signal on the FPA, obtainedfrom an optomechanical simulation of the system [55]. The X/Y scaling is ±50 microns ineach case. The beacon PSF is much sharper due to good collimation and focusing but also in-cludes background noise from the Earth as seen by the ripples over the plane. The calibrationPSF is more spread due to imperfect collimation but contains negligible background noise asit is being generated internally.

The FSM can be mechanically tilted by ±3 degrees in both axes which allowsfor ±6 degree steering of the internally generated beam, as the optical tilt angleis twice the mechanical angle by definition. This is well within the expected hostsatellite pointing error. Moreover, in the maximum of the steering range, thebeam of the calibration laser is too displaced after multiple reflections (FSM, flat


side mirror, dichroic mirror) and does not hit the focusing lens aperture due togeometrical constraints. This limits the visibility of the feedback signal to about±5 degrees on the FPA.

Transmission Path

NODE is designed so that the transmission signal experiences minimal loss on theinternal optics. Both the WDM and the collimator are factory-calibrated for itswavelength, the loss on the FSM and the dichroic mirror is very low as well as onthe bandpass filter. The well-collimated beam can be steered within the full fieldof regard of the FSM and it exits the aperture with a FWHM divergence of 1.3mrad per the collimator parameters.

A more comprehensive depiction of the pointing system’s FOV with regards toeach signal is shown in Figure 3.8 below. As it can be seen, there exists a regionin which the beacon is detectable but is not addressable by the transmission beam(due to FSM throw) and by the calibration laser (due to geometrical constraints).However, these regions are well beyond the expected host coarse pointing capa-bility and thus can be neglected. The FSM throw was chosen as a trade-off sothat certain extra margin is kept but also the pointing angular resolution is notdecreased due to a very wide steering range.

Figure 3.8: Analysis of the pointing system’s FOV.

26 APPROACH

3.2 Pointing Control Concept

From a control theory standpoint, the pointing system is not meant to settle ona static value, but rather follow a varying setpoint given by the beacon’s angle ofincidence (off-boresight angle), which will drift as the host satellite’s body pointingis disturbed. Consequently, the information that determines the desired pointingvector is the centroid of the beacon spot image on the FPA.

Similarly as in Figure 3.3 and Equation 3.1, we know that for a beacon signalwith an angle of incidence θB at the satellite aperture, the following holds:

tan θB =| ~dB|f

(3.2)

where f is the lens focal length and ~dB is a focal-plane vector from the point wherethe FPA intersects with the lens optical axis (ideally its center) to the point ontowhich the signal rays are focused - the centroid of the beacon spot. The controlgoal is to align the transmission signal (coupled with the feedback signal) withθB. The pointing is thus optimal when the angle of the internal coupled signal, θC ,equals θB at the satellite’s aperture.

Likewise, for θC , the following holds:

tan θC = tan (2θFSM) =| ~dC |f

(3.3)

where θFSM is the FSM mechanical tilt from its nominal pointing angle and ~dC isa focal plane vector pointing to the centroid of the calibration laser spot.

If we analyze the ray geometry between the aperture and the lens, as is depictedon the left-hand side in Figure 3.9, we find that under optimal pointing, the beaconand the calibration rays are inverted in front of the focusing lens. This is dueto the backwards reflection of the calibration beam from the side mirror. As aconsequence, the vectors ~dB and ~dC mirror each other around a center of symmetryon the focal plane as long as θB equals θC . This is visualized on the right-hand sidein Figure 3.9.

Because of this, the control goal can be written as:

~dC!

= − ~dB (3.4)

At this point, it is useful to switch to the coordinate frame of the camera’s FPAas that is where the centroids will be sampled. The output from the camera isan image with origin in the top-left corner and is of 5 megapixels, 2592 pixels inwidth and 1944 pixels in height. This coordinate frame is also visualized on theright-hand FPA diagram in Figure 3.9.

3.2. POINTING CONTROL CONCEPT 27

Figure 3.9: Depiction of the ray geometry around the dichroic mirror, with the beacon beamin blue and the coupled transmission/calibration beam in red. If the beams are aligned at theaperture, they will have opposite angles of incidence at the focusing lens due to reflection ofthe feedback signal from the side mirror. As a result, the spot of the calibration laser has tomirror the location of the beacon signal around a center of symmetry on the FPA to achievecorrect pointing, as is shown on the right-hand side.

We can now redefine ~dB and ~dC in these new coordinates as points on the image,PB and PC , in pixels and with origin in the top-left corner:

PB = PCENTER +~dBµ

(3.5)

PC = PCENTER +~dCµ

(3.6)

where PCENTER is the location of the center of symmetry in pixels and µ is thepixel pitch. By inserting Equations 3.5 and 3.6 into Equation 3.4, we get:

µ(PC − PCENTER)!

= −µ(PB − PCENTER) (3.7)

which can be reduced and forms the final version of the equation that determinesthe desired value for the centroid of the feedback signal:

PC!

= 2PCENTER − PB (3.8)

28 APPROACH

3.2.1 Center of Symmetry Problem

In an ideal case, the point defining the center of symmetry between the beacon andfeedback centroids, PCENTER, would be in the center of the FPA. This would be thecase if the lens was perfectly parallel with the FPA and its optical axis went exactlythrough its center. In reality, however, this is not necessarily the case, as theremay exist a microscopic mechanical misalignment between the lens and the FPA,which would cause the optical axis of the lens to intersect with a different pointon the FPA, and thus shift PCENTER. Consequently, if this would be neglected, itwould result in a fixed pointing bias, as the calculated PC setpoints would not becompensated for the offset.

Another potentially severe issue is misalignment between the dichroic mirrorand the regular flat mirror on its side. If the angle between these two mirrors is notexactly 45 degrees, or they are not both perfectly perpendicular to the baseplate(vertically), the calibration signal will always have an undesired offset on the FPAthat will skew the FSM pointing feedback. Since the fine pointing system aimsfor the highest possible accuracy, and the pixels have FOV in the order of µrad,microscopic misalignment could significantly worsen the pointing performance inthis case as well. To compensate for this offset, the exact angle of misalignmentwould have to be subtracted from the PC setpoints. Fortunately, this can also beachieved artificially by simply moving PCENTER by a certain static offset, which isanalogous to the lens misalignment problem.

Ultimately, if an appropriate PCENTER is found experimentally with high pre-cision, the control system is capable of compensating for both of the potentialmechanical misalignment problems discussed. As the NODE mechanical structurewill be built with certain machining tolerances, these misalignments should notbe neglected, and finding the correct PCENTER is a crucial step in assuring optimalperformance of the pointing system.

An alternative optical design trade-off study that utilizes a retro-reflector andis also able to overcome these problems is discussed in Appendix A - AlternativeFeedback Design with a Retro-Reflector.

3.3. FSM DYNAMICS & CONTROL 29

3.3 FSM Dynamics & Control

The FSM from Mirrorcle Technologies is a gimbal-less scanning two axis (tip-tilt)MEMS mirror. It is mechanically steered by a set of electro-static actuators thatdissipate less then a few milliwatts of power, and thus is one of the lowest SWaPCOTS beam steering solutions available. The actuators are operated in a modecalled the Bias-Differential Quad-channel (BDQ) mode, where each axis is linkedto a pair of channels and rotated by differential voltage applied on the pair witha certain bias. This methodology is implemented either by custom amplificationelectronics, or a driver optionally provided by the manufacturer.

3.3.1 Feedback Mapping

In order to take advantage of the optical FSM pointing feedback and establisha control loop, a mapping, or transformation, between the measured feedbacksignal centroid position, PC , and the FSM control voltage, VBDQ, is needed.

If such mapping is known, a desired centroid location of the feedback laser, P ∗C ,

can simply be transformed:

(P ∗C,X , P

∗C,Y ) −→ (VBDQ,X , VBDQ,Y ) (3.9)

which immediately enables open-loop steering within the FPA reference frame, asP ∗C can be calculated from Equation 3.8 as long as PB, the beacon centroid, is

being tracked.Likewise, if PC is being tracked simultaneously, then a certain control error:

∆PC = P ∗C − PC (3.10)

can be transformed:

(∆PC,X ,∆PC,Y ) −→ (∆VBDQ,X ,∆VBDQ,Y ) (3.11)

and fed into a controller to establish closed-loop FSM pointing.Ultimately, a mapping that relates the FPA coordinate frame (where PC is de-

fined), to a coordinate frame defining the corresponding inputs, VBDQ, is sought.Since this relationship is very sensitive to the geometrical alignment between theFSM and the FPA, a transformation with more degrees of freedom is desired tominimize the mapping error, as there may exist, for instance, certain rotation be-tween the systems that causes unexpected X/Y axis coupling. Moreover, to enableopen-loop control by mapping the points directly (as in Equation 3.9), a trans-lational degree of freedom is also required as the two frames do not share the

30 APPROACH

same origin: the FPA system has origin in the image edge, whereas the FSM nom-inal zero tilt corresponds to the FPA center (ideally) and it can be steered in bothpositive and negative directions (see the system FOV analysis in Figure 3.8).

To fulfill these criteria, a mapping in the form of an affine transformation (alsocalled an affine map) is chosen. Affine transformation is the most general form of alinear transformation, consisting of two functions: a linear map and a translation.In 2D space, the linear map is determined by a 2-by-2 matrix A and the translationby a 2-by-1 vector t. The affine transformation maps a point P to a new point, Q:[

QX

QY

]=

[axx axyayx ayy

] [PX

PY

]+

[txty

](3.12)

With six degrees of freedom, the affine transformation can cover a superpositionof multiple generic operations. For example, the parameters of the linear map A

can represent frame scaling, rotation, shearing and reflection, while frame trans-lation is determined exclusively by the vector t. An example is visualized in Figure3.10.

Figure 3.10: Illustration of a potential affine transformation between the FPA coordinateframe and the FSM input coordinate system, as described by Equation 3.13.

In our case, we are looking for an affine map between P ∗C and VBDQ:[

VBDQ,X

VBDQ,Y

]=

[axx axyayx ayy

] [P ∗C,X

P ∗C,Y

]+

[txty

](3.13)

This formula corresponds to the mapping needed for open-loop control as shown


in Equation 3.9. For closed-loop FSM control (Equation 3.11), the translationvector t is cancelled out because differences (i.e. control errors) are used, whichsimplifies the formula to:[

∆VBDQ,X

∆VBDQ,Y

]=

[axx axyayx ayy

] [∆PC,X

∆PC,Y

](3.14)

The matrix A is in this case sometimes referred to as the sensitivity matrix.An approach for the actual determination of the transformation parameters is

outlined and derived in Section 3.5 - Calibration Algorithm.

3.3.2 Pointing Modes

With a conceptual feedback mapping in place, a simple open-loop pointing chaincan be set up, as is depicted in the block diagram in Figure 3.11 below.

Figure 3.11: A high-level block diagram of open-loop FSM pointing.

In this case, the camera is used solely as a beacon detector, tracking only thebeacon centroid PB. The beacon centroid is used to calculate P ∗

C , the desiredvalue of PC (even though the calibration laser is turned off or not sampled) tofollow the pointing concept. This value is then transformed into the FSM-space,and a control voltage is obtained and applied to the FSM after each sample.

Correspondingly, if the camera samples both the beacon and the feedback signalsimultaneously, a closed-loop pointing control chain can be established. In thiscase, the control error is transformed using Equation 3.14, which gives the neededcontrol error in FSM-space as a voltage. A simple discrete integral controller isthen utilized to drive the FSM voltage, as the expected pointing disturbance isinherently slow and continuous. The integral term assures minimization of thesteady-state error and compensation of potential nonlinearities in the system.

There are benefits and downsides for both of the control modes. The open-loopchain is very simple to implement if the feedback mapping is calculated. In thisregime, only the beacon spot is sampled, so only a small fraction of the FPA needsto be read out continuously, which can be achieved with the camera windowing

32 APPROACH

Figure 3.12: A high-level block diagram of closed-loop FSM pointing control. An integralcontroller is utilized to correct for steady-state error calculated using the feedback signal.

functionality. This has the potential to considerably increase the sampling rate, asthere is no need to sample the calibration spot, which is also bigger in size dueto the optical properties of the system. The number of pixels to be sampled istherefore certainly less than half of what would be needed for closed-loop control,which leads to more than double the sampling rate. Moreover, if the calibrationlaser is turned off, there is no chance the two signals can interfere with each otheron the FPA. On the other hand, the pointing accuracy of the open-loop modeinherently depends on the accuracy of the a priori calculated affine map. Any un-certainty in the map, or in a certain region on it, will directly cause a steady-stateerror that cannot be compensated. It is also unable to deal with any misalignmentintroduced throughout the control process, such as mechanical shifts caused bythermal expansion, which could make the affine map gradually obsolete. Hence,the open-loop chain lacks a certain robustness and is not very favorable.

The closed-loop mode is obviously more challenging to implement as the detec-tor needs to sample two different signals simultaneously. Consequently, samplingrate is decreased and problems with interference can also arise, which potentiallyfurther increases implementation difficulty. The major benefit, however, is thatthe controller ensures rejection of steady-state errors. Even if the affine map haslocal uncertainties, e.g. due to neglected nonlinearities, the integral controller willmake up for the introduced pointing errors. In addition, should temperature vari-ations during fine pointing disrupt the optical alignment, the sensitivity matrix canbe potentially updated continuously with new measurements from the calibrationlaser, and thus “learn” for gradual alignment changes in an adaptive fashion.

The pros and cons of the control modes are summarized in Table 3.1. Ultimately,both pointing regimes are to be implemented, with the closed-loop mode being


Table 3.1: Summary of pros and cons between open-loop and closed-loop FSM control.

Open-Loop FSM Control Closed-Loop FSM Control+ simple implementation + error always converges to zero+ higher sampling rate + can adapt to thermal shifts+ no signal interference – more complex implementation– errors in steady state exist – potential signal interference– cannot adapt to thermal shifts – lower sampling rate

favored for its higher accuracy and robustness.

3.3.3 Dynamic Model

In order to tune the closed-loop controller optimally, the dynamics of the processchain need to be modeled. Modeling of the FSM itself is significantly simplifiedbecause the manufacturer provides each unit with a unique datasheet, where theFSM frequency characteristics measured during its factory calibration are docu-mented. This allows for a quick determination of the FSM transfer function with-out the need to perform any system identification process.

For us, the two main parameters of interest are the FSM resonant frequency,w0, and its quality factor Q, which is analogous to the damping ratio. Based onthese two parameters, the dynamics of the FSM can be modeled as a dampedmechanical oscillator using a second order transfer function simply as:

θFSM(s)

VBDQ(s)=

w20

s2 + w0

Qs+ w2

0

(3.15)

Notably, because of a highly resonant step response, the manufacturer recom-mends usage of an analog low-pass filter (LPF) at the FSM input. The customdatasheet also provides the recommended cut-off frequency given the unique fre-quency characteristics. This LPF is to be included in the amplification electronicsused to drive the FSM voltage. The driver provided by Mirrorcle Technologiesalready incorporates a 6-th order Bessel LPF for every of the four BDQ outputvoltages. For the dynamic model, the LPF is modeled in the MATLAB environ-ment using the besself function in the Signal Processing Toolbox, from which thefilter’s transfer function is obtained based on its order and cut-off frequency.

To make sure the values are correct and the model is representative, we an-alyze its step response with and without the inclusion of the LPF, as shown inFigure 3.13. Comparing the modeled response with the real response measuredby Mirrorcle Technologies, we find an identical match and thus assume a sufficientrepresentation of the FSM dynamics for our needs.

34 APPROACH

0 5 10 15 20

Time, t (ms)

0

0.5

1

1.5

2

No

rma

lize

d o

utp

ut,

F

SM

FSM Model Step Response

No Filter 200 Hz LPF

Figure 3.13: Step response of the dynamic FSM model with and without a LPF on its input.

The last dynamic element from the chain is the camera, which samples the beamsteered with the FSM. Since the camera is based on CMOS silicon photodiodes,the pixels have response times on the order of nanoseconds. While the cameraitself dictates the sampling rate due to the large number of elements and thenecessary exposure time, the dynamic response of each pixel is almost negligiblewhen compared to the rather slow dynamics of the FSM. Consequently, we do notfocus on modeling the dynamic response of the FPA, but instead, as a next step,model some of its other properties that more severely influence the control chain,such as readout noise and potential lag between frame capture and final centroiddetermination.

3.3.4 Controller Tuning

Following the determination of the dynamic system model, we continue by inves-tigating it inside a control loop simulated within the MATLAB Simulink environ-ment, so that a controller with suitable performance can be obtained. A typicalrecursive backward-Euler discrete integral controller is utilized:

I(z) = KI Tsz

z − 1(3.16)

where KI is the tunable integral constant and Ts is the control loop sampling time.The control loop simulation is further augmented by a quantizer to represent

the digital-to-analog converter (DAC) resolution available in the mirror driver andby elements in the sampling chain. These include the readout noise, the FPA


sampling rate and an artificial sample delay which is expected due to the cameraUSB interface and algorithm execution under a non-real-time operating system3.While the transfer functions were determined primarily in an analytical way, theseblocks are tuned mostly after experimental measurement trials with the actualbeacon camera, which are further discussed in Chapter 4. The complete controllertuning simulation scheme is depicted in Figure 3.14.

FSMLPF Scope

TransportDelay

I(z)

ControllerStep DACQuantizer

FPASampling

ReadoutNoise

Figure 3.14: Simulation scheme used to tune the discrete integral controller.

The controller is tuned by analysis of its reference tracking capability using theControl Design Toolbox within Simulink. It has to be taken into consideration,however, that this simulation scheme does not account for inaccuracies that mayexist in the feedback mapping, i.e. the feedback signal is directly used in the loopwith unity gain. Moreover, slow frame rate and the non-real time nature of the sys-tem that leads to the transport delay between frame capture and eventual centroidcalculation makes the system very sensitive to instabilities. A more conservativeapproach in the controller tuning is therefore taken, so that a stable, albeit slowerresponse is maintained.

3The control loop and associated image processing algorithms are running as a process underthe Linux operating system.

36 APPROACH

3.4 Detector Sampling

Before a controller can be implemented on the payload hardware, a techniqueto obtain and track centroids from the FPA exposures has to be developed. Inthis section, the approach on the sampling of the detector is presented, includingcentroid determination, its tracking, and beacon acquisition logic. Furthermore,an approach that enables simultaneous tracking of the two centroids, PB and PC ,without significant mutual interference, is presented.

3.4.1 Frame Processing

The initial processing step is primarily focused on the determination of the cen-troids of the laser signals within the FPA, or a certain region of it. Given thatthe camera outputs a matrix of 10-bit values, an image processing algorithm thattransforms this intensity map into 2D positional information is necessary. To makethis procedure as flexible and reliable as possible, it was split into three indepen-dent phases: thresholding, grouping, and centroiding.

Phase 1: Thresholding

In the first phase, thresholding of the frame is performed, which discards all pixelsbelow a certain determined intensity of significance. This leads to two benefits: itdramatically reduces the number of active pixels considered for further process-ing, and it also helps reject background noise that might add uncertainty to thecentroid calculation.

To work reliably under a variety of SNRs, a unique threshold is calculated basedon the properties of each frame that is captured. Since by design, a vast majorityof each frame is the background, the mean intensity is utilized in the thresholdcalculation. This gives a good starting value, which is analogous to the averagebackground noise intensity, albeit slightly biased upwards if there is a laser spotpresent. This value is then further offset by a small intensity offset to reject peaksin the noise distribution and used as the final intensity threshold.

This approach leads to the following threshold formula:

hthreshold =1

WH

(W∑i=1

H∑j=1

hij

)+ hoffset (3.17)

where h is a specific intensity and W and H is the frame width and height in pixelsrespectively.

3.4. DETECTOR SAMPLING 37

Phase 2: Grouping

In the second phase, neighboring pixels that remained after the thresholding pro-cess are grouped together. As the shapes of the laser spots are continuous bynature, this step separates them from any potential leftover disturbances in theframe. A group size check is also performed, and groups that contain a negligibleor extreme amount of pixels are discarded. This further helps to isolate the wantedsignal and also serves as a technique to discard potentially radiation-damaged pix-els that are stuck in a saturated state, also referred to as hot pixels. Finally, thegroups are sorted by their maximum intensities in a descending order.

Phase 3: Centroiding

In the last phase, the actual centroid of each group is calculated using a standardcenter-of-mass formula:

Pk =1

Nk

Nk∑i=1

hk,i pk,i (3.18)

where Pk is the centroid of the k-th group, Nk is the number of pixels in thatgroup, hk,i are the individual pixel intensities and pk,i are the pixel X/Y indiceswithin the FPA. The final result from the initial frame processing algorithm is thusa list of pixel centroids sorted by brightness, serving as a prioritized “candidatelist” for the sought signal in further processing.

3.4.2 Sampling Scheme

With a technique to process the raw data obtained from the FPA, we focus onthe high-level sampling approach. In particular, the beacon acquisition and thesubsequent centroid tracking logic is investigated.

Acquisition

Before the centroid tracking process can begin, the initial beacon signal has to beacquired. For this reason, a beacon acquisition procedure is designed and ran dur-ing which the calibration laser is disabled. The core of this procedure is continuoussampling of the whole FPA, while sweeping the exposure time and performing fastsanity checks on the frame histograms. If the sanity checks pass, the frame pro-cessing algorithm is executed and if a good signal candidate is found, acquisitionis declared successful.

The exposure sweep is continuously performed in a rapid manner, so that thereis a high chance of getting proper acquisition parameters for a wide range of

38 APPROACH

beacon powers4 quickly, where the detector is neither too saturated nor readingzero. After each image is obtained, its histogram is calculated and two fast sanitychecks are performed:

1. The highest intensity recorded in the histogram is verified. If this value isabove a certain acquisition intensity threshold, the check passes.

2. The distance between the histogram maximum and the highest intensity isverified. This value serves as a good indication of whether a signal with suf-ficient SNR is present in the frame, such that it can be processed successfully.If the distance is above a certain threshold, the check passes.

If any of the checks fails, the frame is discarded and a new sample is immediatelyrequested with adjusted exposure. If both of the checks pass, the frame processingalgorithm is ran, which returns the potential signal candidates. If no centroidsare found5, the frame is discarded and the acquisition procedure continues untila signal is found. Ultimately, if a good centroid is obtained from the processingalgorithm, the beacon acquisition concludes successfully.

Straight after the beacon is acquired, the exposure time is fine-tuned for itspower, and a window (i.e. region on interest) around the spot is determined forfurther sampling. In the next step, using the acquired PB, the desired value ofPC is calculated following Equation 3.8, and initial pointing is set using the open-loop control mode. The feedback laser is then turned on and can be acquired onthe detector in the given location. After both signals are acquired, the acquisitionphase ends and the tracking phase can begin.

Tracking Logic

With the initial locations known, the centroids are tracked following a double-window sampling methodology. The core idea of this technique is that the camerais reconfigured after each frame to sample either a window around the beaconspot, or a window around the calibration laser spot, with exposure time unique toeach window. The signals are sampled in an alternating fashion, such that a snap-shot of the beacon is followed by a snapshot of the calibration signal, followed bya snapshot of the beacon again, and so on. This is visualized from the perspec-tive of the FPA in Figure 3.15. Consequently, the request and update chain on thedetector can be illustrated as shown below.

Acquisition −→ Request PB −→ Update PBRequest PC

−→ Update PCRequest PB

−→ Update PBRequest PC

−→ · · ·4The received beacon power will vary greatly due to change in distance during an overpass.

Weather conditions may also severely affect the power during an overpass.5This might also be the case when the frame is overexposed.

3.4. DETECTOR SAMPLING 39

Figure 3.15: Illustration of the double-window sampling technique. The beacon and thefeedback signals are sampled independently in an alternating fashion. Each signal is sampledwith a different exposure window within the FPA that is adapted based on the location andpower of the signal. The windows are switched after each sample so that both signals aresampled with a static rate.

After each sample update, the parameters for the respective window are recalcu-lated iteratively, in order to adapt to the signal location and power changes. Thistechnique is very advantageous, as it increases the sampling rate significantly dueto the small window size that needs to be sampled in each step. Moreover, anypotential disturbances outside of the small windows are immediately avoided anddo not disturb the frame processing procedures.

To further maximize the tracking reliability, the properties of a signal are savedfrom its former sample and then compared with the properties of each candidatefrom the next sample. Properties such as spot size, its location and intensity,are evaluated against each signal candidate that the frame processing algorithmreturns. The candidate with the closest match is then selected as the sought signal.This allows for uninterrupted tracking of a signal, even in the case if anothererroneous signal with higher intensity appears in the sampled FPA window.

Signal Loss

There is a substantial likelihood that a signal loss scenario might occur duringan overpass. This is especially due to potential cloud coverage that might lead tounexpected beacon fading and drop the SNR below a detection threshold. Becauseof this possibility, a procedure that restarts the acquisition process depending ona specified duration of the signal loss is implemented. This procedure is then

40 APPROACH

executed if the saved parameters of the last valid sample are considered to be toooutdated for confident continuation in the described tracking technique.

3.4.3 Minimizing Interference

It is anticipated that the beacon and the calibration signals might interfere witheach other on the FPA. This will happen when the beacon signal will be in closevicinity of the center of symmetry around which the calibration signal mirrors it,i.e. PB will be converging to PCENTER. If this distance becomes low enough thatthe spot of the calibration beam will start overlapping with the spot of the beaconbeam, the frame processing algorithm may fail to isolate them.

This is especially dangerous for samples of the beacon signal, as the calibrationlaser spot is bigger and might entirely cover it. Moreover, the beacon power,and thus the exposure time of its sampling window, may vary rapidly. On theother hand, the power output of the calibration laser is designed to be constant,so it might happen that their window exposure times will differ significantly. Ifthe spots are close, this might lead to an extreme situation, where the beaconsampling window will also contain the calibration signal, but sampled with suchhigh exposure time that it will saturate the window completely.

To minimize this interference as much as possible, a feedback switching mecha-nism is implemented. The central idea is that the calibration laser is switched offduring the beacon readout phase and then switched back on before a snapshot ofitself is requested. Consequently, in the beacon readout phase, only the beacon sig-nal is hitting the FPA, while during the feedback readout, both signals are present.This solves the biggest potential issue that was described earlier. However, whenthe feedback signal is sampled, it might still suffer from slight interference fromthe beacon signal, depending on its power. For this reason, the power of the cali-bration laser is fine-tuned in hardware such that it can be reliably sampled usingthe lowest possible exposure time of the detector, which is orders of magnitudelower than the exposure needed for the beacon, even at the highest satellite ele-vation angle. Ultimately, even if the spots theoretically “cover” each other in thefeedback readout phase, due to the extremely low exposure used in its samplingwindow, the interference from the beacon photons will be almost negligible.

A high-level visual summary of the sampling scheme together with all the otherpointing control elements is presented in the concluding Section 3.6 - Summary.

3.5. CALIBRATION ALGORITHM 41

3.5 Calibration Algorithm

The earlier outlined optical feedback mapping is one of the most sensitive andcrucial elements of the entire pointing control chain, as it facilitates utilizationof the calibration laser for both open-loop and closed-loop FSM control. In anideal case, where the optics are perfectly aligned, it is possible to analyticallycalculate both the sensitivity matrix A and the translation vector t using the FSMvoltage vs. mechanical angle characteristics and the lens and detector parameters.However, as hypothesized in Section 3.2.1, perfect alignment is not expected andso potential misalignment should be accounted for to achieve optimal pointingprecision. For the affine map in particular, misalignment introduces uncertainty inthe vector t, but also in the linear map, for instance in the form of axis rotation.Because of such sensitivity to the system geometry, and especially the fact that thisgeometry might be disturbed during and after the satellite launch due to shockand vibration, a more robust and accurate approach to obtain the affine map isdesired.

The proposed solution is to develop a calibration algorithm that will estimatethe transformation parameters based on an automated measurement, which canbe ran at any point on orbit. This measurement can collect a certain amount ofcorresponding points in the two systems (i.e. landmarks in a sense) and thennumerically estimate the transformation using the collected pairs. As it would beoptimal to run the calibration directly before the transmission and fine pointingbegins, the algorithm runtime is also considered as a relevant attribute besides theestimation accuracy.

3.5.1 Parameter Estimation

With six degrees of freedom, a minimum of three source points (in the FPA system)and three corresponding target points (in the FSM system) are necessary for fulldetermination of the affine map. This would give a balanced set of equations thatcan be solved directly:

AP1 + t = Q1

AP2 + t = Q2

AP3 + t = Q3

(3.19)

However, this is not a very redundant solution, as a single errant correspondenceprofoundly affects the entire transformation. It is also very sensitive to the camerareadout noise, which is inherently random and can add undesired uncertainty tothe map. A more favorable approach is to collect a higher amount of points andthen estimate the parameters more optimally by minimizing the total transforma-

42 APPROACH

tion error. Consequently, using an arbitrary number of source and target points,we get an overdetermined equation system:

AP1 + t = Q1

AP2 + t = Q2

...

APN + t = QN

(3.20)

To derive an optimal transformation from the set in a least-error sense, a mini-mization of the following error criterion is sought:

f(A, t) =N∑i=1

‖APi + t−Qi‖2 (3.21)

which is a standard least squares fitting problem. The purpose is to find a solutionover all possible 2-by-2 matrices A and all possible 2D-vectors t such that thegradient of f vanishes.

With the following denotations:

P =1

N

N∑i=1

Pi (3.22)

Pi = Pi − P (3.23)

where P is the center of mass of a set of points, and Pi denotes the thereaftercentered points, it can be shown with an intrinsic proof (derived in [61]) that thegradient of f vanishes for the following A and t:

A =

(N∑i=1

Qi Pti

)(N∑i=1

Pi Pti

)−1

(3.24)

t = Q− AP (3.25)

The calculation is valid for any number of corresponding point pairs equal orhigher than 3, which are not contained within any sub-space of the transformedsystem, for instance on a straight line. This gives the calibration algorithm goodflexibility, as the number of points to be collected can be chosen at will dependingon the desired accuracy and algorithm runtime.

3.5.2 Data Collection

To obtain the necessary data for the calculation, an automated measurement isperformed, which gradually changes VBDQ while tracking the resulting PC on the

3.5. CALIBRATION ALGORITHM 43

detector. To facilitate this measurement, the FSM is steered in a spiral pattern, asvisualized in Figure 3.16. This approach has several advantages. Firstly, it is veryeasy to implement in a parameterized way, such that the number of points andtheir density can be tweaked easily using the frequency of the sines and cosines.Secondly, by standard definition, the density of the points is decreasing outwardsfrom the center, and thus the lowest local uncertainty should correspond to thecenter of the steering range. This follows the assumption that statistically thepointing disturbance is expected to have a normal distribution around zero. Lastly,the measurement can be performed in a single continuous motion without unnec-essary revisits or big voltage steps, and so is quite time and space efficient.

-1 -0.5 0 0.5 1

Normalized X Voltage, VBDQ,X

-1

-0.5

0

0.5

1

No

rma

lize

d Y

Vo

lta

ge

, V

BD

Q,Y

100 pts Spiral Pattern

-1 -0.5 0 0.5 1

Normalized X Voltage, VBDQ,X

-1

-0.5

0

0.5

1

No

rma

lize

d Y

Vo

lta

ge

, V

BD

Q,Y

500 pts Spiral Pattern

Figure 3.16: An example of two different spiral measurement patterns used to collect data forthe affine map determination.

3.5.3 Implementation

The overall algorithm can be summarized in a few major steps. In the initialphase, the FSM-system points are generated based on the desired total count ofcorrespondences, N . Let:

n = [0, 1, 2, ..., N − 1] (3.26)

a =VBDQ,max

N − 1n (3.27)

44 APPROACH

ω = π

√N

N(3.28)

where n is a vector of point indices, a is a growing vector of amplitudes scaled tothe FSM maximum voltage, VBDQ,max, and w is an angular frequency function ofchoice that defines the spiral point distribution. We then define the FSM-systempoints as:

VBDQ,X,i = ai cosωni (3.29)

VBDQ,Y,i = ai sinωni (3.30)

which together gives VBDQ,i, the i-th point in the measurement pattern, as visual-ized in Figure 3.16.

Next, the FSM is steered continuously using each VBDQ,i, and after each update,the resulting feedback laser centroid, PC,i, is saved to memory. Ultimately, afterall the N corresponding points are collected, the general transformation from adesired P ∗

C to VBDQ is calculated:

A =

(N∑i=1

VBDQ,i PtC,i

)(N∑i=1

PC,i PtC,i

)−1

(3.31)

t = VBDQ − APC (3.32)

After A and t is obtained the algorithm concludes and the feedback can bemapped accurately within the control chain. Experimental results of the perfor-mance of this algorithm are summarized in Chapter 4.2 - Calibration & AcquisitionTesting.

3.6. SUMMARY 45

3.6 Summary

In conclusion, we present a short top-level analysis of all the techniques thatwere designed to enable robust implementation of the whole fine pointing con-trol chain, and look at how these sub-processes interact.

The initial process that is executed at the beginning of the pointing chain (i.e.before the satellite overpass) is the calibration algorithm. This is vital, as thecontroller performance depends on having an accurate optical feedback mapping,which in turn depends on the current system alignment. The algorithm is ranwith the feedback laser turned on, and performs an automated measurement,in which the frame processing algorithms are utilized to find correspondencesbetween input voltage and output feedback centroid configurations. The resultingmapping is then used each time the FSM is moved to achieve precise steering.

After the calibration concludes, the feedback laser is turned off and the systemis ready to begin pointing control as soon as a beacon signal is acquired. For thisreason, a robust beacon acquisition procedure is ran until a valid signal is obtainedon the FPA. The procedure rapidly sweeps the FPA with different exposure timesand performs fast sanity checks to determine if the frame can be potentially pro-cessed successfully. If a good signal candidate with correct properties is obtainedfrom the frame processing algorithm, acquisition is declared successful.

With the initial beacon location on the FPA, the actual tracking and controlscheme begins. The system is designed to allow both open-loop and closed-loopFSM pointing. In either case, the beacon spot is sampled with a small adaptivewindow on the FPA to increase the sampling rate, and robust tracking algorithmsare utilized to provide reliable centroiding by evaluating the signal properties inbetween samples. In the open-loop mode, the FSM is steered immediately aftereach beacon sample using the affine map. In the closed-loop mode, the feed-back laser is turned on and sampled after each sample of the beacon signal inan alternating fashion. The control error is then determined using the calibratedsensitivity matrix, and the FSM is driven by a discrete integral controller to rejectpointing error.

In the case of a total signal loss, the tracking and control process is interrupted,and the system switches back to the beacon acquisition phase. The whole chain isvisualized in a block diagram in Figure 3.17.

46 APPROACH

Figure 3.17: A high-level block diagram of all the major processes in the pointing controlchain, showing both of the possible control modes and the associated branching logic.

CHAPTER 4

Experiment

To test and verify the fine pointing algorithms, a laboratory setup is assembledbased on the optical design and selected payload electronics. The control chainis then implemented on the payload microcontroller (PMC), and each process inthe chain is verified. The testbed itself is summarized in Section 4.1, followed byexperimental results of the calibration and acquisition processes in Section 4.2.Next, Section 4.3 focuses on precise measurement of PCENTER, which is necessaryfor optomechanical misalignment compensation. Lastly, Section 4.4 and 4.5 coverthe approach and results from the pointing accuracy verification.

4.1 Testbed Assembly

The testbed is built based on the design and optical hardware described thor-oughly in Section 3.1. The primary optical components are mounted on an opticalbreadboard and manually aligned. This includes the beacon camera, focusinglens, dichroic and regular mirror, FSM, and collimator (Figure 4.1). The optics aremounted such that they are spaced as closely as possible to the NODE mechanicalstructure design. The beacon camera is connected to the PMC using a standardUSB interface. The FSM is wired to a mirror driver from Mirrorcle Technologies,which contains a DAC and a tunable LPF to facilitate the FSM operation. Thedriver itself is commanded over a serial peripheral interface (SPI) bus from thePMC, and the LPF cut-off frequency is set with a clock that is generated using apulse width modulation (PWM) output on the PMC.

The calibration path is closed using two optical fibers which connect the colli-mator to a fiber-coupled 635 nm laser source through a WDM. The second WDMinput port is left unconnected, since the transmission laser is not required forpointing experiments. The calibration laser source is connected to the PMC us-

47

48 EXPERIMENT

Figure 4.1: Mounted optical components in the initial laboratory testbed. The componentsare mounted to be as close as possible to the designed NODE mechanical structure.

ing an analog modulation port, which allows the PMC to control its on/off stateusing a general purpose input/output (GPIO) pin. To imitate the beacon signal,another collimated 635 nm laser source is set up independently in the camera’sFOV for initial testing. A functional diagram that depicts the interfacing betweenthe components can be seen in Figure 4.3.

4.1.1 Initial Hardware Testing

The testbed was used to test a lot of preliminary embedded software, mainly fo-cused on the FSM operation and the beacon camera configuration. The cameraoffers the capability to sample sub-regions of the FPA for faster readout (win-dowing), and also neighbor-pixel averaging (binning) to increase readout whilesacrificing resolution. To test its performance, a frame rate measurement was ranunder all the possible windowing and binning configurations. The results are de-picted in Figure 4.2. It can be seen that the frame rate increases exponentiallyfor smaller window sizes, which further motivated the double window samplingapproach that was designed. A significant rate boost can also be seen with higherbinning modes, which motivated the usage of binning in the beacon acquisitionalgorithm, during which high resolution is not necessary.

Another measurement investigated the effect of camera configuration changes

4.1. TESTBED ASSEMBLY 49

0 500 1000 1500 2000

Window size (px)

0

100

200

300

400

500

Fra

me r

ate

(H

z)

Detector sampling performance

Binning offBinning 2x2 AVGBinning 4x4 AVG

Figure 4.2: Measured sampling rate of the beacon camera as a function of the sampled win-dow size (i.e. width). The measurement was performed for all the available camera binningmodes using a one millisecond exposure time.

between samples on the overall sampling rate. This included the window locationand exposure time as a continuously varying parameter. It was found that the cam-era trigger mode plays a crucial role in the case where configuration is changedrapidly. By default, the detector uses a continuous trigger, which struggles if theconfiguration is continuously updated. The alternative on-demand trigger hasproven to be much more optimal for this case. A summary of some measurementscan be seen in Table 4.1. While continuous trigger outperforms the on-demandtrigger in static configuration cases, it becomes extremely slow for varying con-figurations. As the designed sampling technique is based on switching betweenwindows and exposure times after each sample, the on-demand trigger is pre-ferred.

Table 4.1: Sampling rates of the camera under varying sampling configurations.

Sampling configuration Continuous trigger On-demand triggerStatic 100 px window 330 Hz 265 HzMoving 100 px window 40 Hz 110 HzVarying exposure full-frame 4 Hz 16 Hz

50 EXPERIMENT

Initial testing of the camera under different configurations also revealed that a 1mW calibration laser source is too overpowered, as it saturates the beacon detectorwhen using the lowest possible exposure time, even after all the optical losses.Consequently, it was decided to add a variable inline fiber attenuator betweenthe laser source and the WDM. This prevents the detector saturation, and allowsfine-tuning the power of the free-space signal, such that it can be reliably sampledusing the lowest exposure setting to minimize the beacon-feedback interference,as discussed in Section 3.4.3.

Lastly, after initial trials, an external graphical user interface (GUI) was devel-oped to facilitate monitoring and debugging of the embedded pointing algorithms.The GUI is running on an external computer connected to the PMC through a se-rial universal asynchronous receiver-transmitter (UART) interface. Flexible com-munication with the PMC is achieved using the Point-to-Point Protocol (PPP). Asummarizing functional block diagram of the interfaces between each componenton the testbed is shown in Figure 4.3 below.

Figure 4.3: Interfacing of components in the laboratory testbed. A variable fiber attenuatoris added to lower the calibration laser power, together with a link to a GUI used for softwaredebugging and monitoring on an external laptop.

4.2. CALIBRATION & ACQUISITION TESTING 51

4.2 Calibration & Acquisition Testing

As a first major experiment, the designed FSM calibration algorithm was imple-mented on the PMC and tested on the optical testbed. Multiple measurementswere ran with different N – the number of collected corresponding points be-tween the FSM and FPA systems – to verify how accurately, and how fast can thefeedback mapping be estimated. The test procedure was as follows:

1. Run the calibration algorithm configured for collection of N point pairs.

2. Densely re-visit different points on the FPA using the estimated mapping.

3. Compare output centroids to input locations to evaluate mapping errors.

This procedure enabled the construction of a 2D calibration error map acrossthe FPA region of interest, as is shown for different configurations in Figure 4.4.An RMS mapping error (RMSE) was calculated for each test run as the primaryfigure of merit. The time needed for the calibration algorithm to complete wasalso measured. The experiment results are summarized in Table 4.2.

Table 4.2: Results obtained from the calibration algorithm experiments.

Configuration Runtime (s) RMSE (px) RMSE (µ-rad)10 point pairs 6.6 2.5 24450 point pairs 8.2 1.4 137100 point pairs 10.9 1.0 98500 point pairs 28.8 1.0 981000 point pairs 49.3 1.0 98

It can be seen that when more than roughly 100 points are used for the estima-tion, the accuracy of the map remains at 1 px RMSE, which is the best mappingaccuracy achieved. The angular RMSE results are consistent with associated re-search done in [50,53], which investigated the FSM tip/tilt repeatability and othersources of potential open-loop pointing error. Given these results, it is hypothe-sized that with correct alignment, an overall pointing accuracy of roughly 100µrad should be achievable even in the open-loop pointing mode, which alreadyfulfills the pointing requirement with a lot of margin. Ultimately, the 100 pointconfiguration was chosen as the default calibration procedure. With a quick run-time of about 10 seconds, it can be easily run after the payload is woken fromstandby before the satellite overpasses the OGS.

52 EXPERIMENT

Figure 4.4: Comparison of calibration errors for affine maps estimated using different numberof point pairs. The color represents re-visit errors for locations on the FPA when the FSM wascommanded in open-loop using the affine map. The darker the color, the better the mappingis for a given pixel. RMS calibration errors are calculated for each case. It can be seen that a100 pts estimation has already the same accuracy as a 1000 pts estimation.

Further experiments also focused on the beacon acquisition procedure. Theexposure sweep, which is done to ensure good conditions for acquisition under anybeacon power, was fine-tuned for the power range obtained from the beacon linkbudget simulation. The minimum and maximum expected beacon power (basedon satellite elevation) was reproduced in the lab to find the rough exposure timerange needed on the detector, with certain added margin. This range was thensplit between ten continuous samples, which results in acquisition times less thenone second long (see full-frame rate in Table 4.1), and is versatile enough to makethe frame processing chain perform correctly.

4.3. CENTER OF SYMMETRY DETERMINATION 53

4.3 Center of Symmetry Determination

In this section, we describe an experimental procedure that was developed forprecise determination of the point PCENTER. As discussed in Section 3.2.1, preciseknowledge of PCENTER is critical to reject errors introduced by optomechanicalmisalignments in the system. If PCENTER is calibrated well, pointing bias due tolens-FPA axis misalignment, as well as due to dichroic-to-side-mirror misalignmentcan be compensated by the controller software.

To experimentally determine the optimal PCENTER, a setup that can indepen-dently measure the angle between θB and θC with high precision outside of thesystem is built. Afterwards, PCENTER can be varied manually during a pointingtest (with the control loop engaged), until θB and θC are equal, which means theoptimal PCENTER has been found.

To measure the angle between the two beams, we utilize a second detector ontowhich the rays are reflected from a beamsplitter, which is placed outside of theaperture. A retro-reflector is used on one side of the beamsplitter so that bothsignals share the same path onto the detector. This ensures that if the signals havethe same angle of incidence at the NODE aperture, they will be focused to thesame point on the external FPA, as is illustrated in Figure 4.5 below.

Figure 4.5: An external optical setup used to measure the angle between the beacon and theoutgoing NODE signal. A retro-reflector prism is used to screen both of the signals on a singleFPA without misalignment issues. This setup enables software calibration of the controller toremove pointing bias due to optomechanical misalignment inside the primary NODE setup.

54 EXPERIMENT

To experimentally obtain the optimal PCENTER, a simple procedure is followed:

1. The main NODE testbed pointing chain is ran with a default PCENTER set tothe center of the FPA.

2. The external setup is used to check the bias in the pointing, i.e. if there is anoffset between the two centroids on the camera.

3. PCENTER is adjusted continuously from the GUI while the pointing controlloop is engaged. This will shift the feedback centroid on the external FPA.

4. Once the spots are exactly at the same point on the external FPA, the beamsare aligned, and the optimal PCENTER has been found.

A longer 125 mm focal length lens is used with the external camera to decreaseits FOV, and thus improve angular resolution, so that the beams can be alignedwith higher precision. The detector is the same as the one used in the primaryNODE hardware. With this configuration, the beams can be aligned within ap-proximately 1 µrad, which is more than sufficient.

This procedure also generally serves as a good check of the alignment qualityin the optomechanical structure. Since the pointing testbed assembled during thisthesis is manually aligned, big PCENTER offsets of up to several tens of pixelswere observed, which is already on the order of a mrad of pointing bias. Whenthe optics will be mounted on the actual structure of the engineering model ofthe payload, the bias is expected to be much smaller, mainly determined by themachining accuracy of the optomechanical mounts. The procedure is also a goodmeans of testing how well can the system preserve alignment e.g. after vibrationor thermal vacuum testing, which is planned in the near future.

4.4. DISTURBANCE SIMULATION 55

4.4 Disturbance Simulation

To begin with the verification of the pointing control loop performance, a way ofsimulating the spacecraft body pointing error in the laboratory is needed. Since avarying body pointing error on orbit will be effectively seen as drift of the beaconcentroid on the NODE FPA, we can accomplish the same by using a second externalFSM, which will steer the beacon signal generated in the laboratory.

Thus, we augment the testbed with another FSM from Mirrorcle Technologiesplaced on the optical axis of the main focusing lens. The FSM is placed at 45degrees relative to this axis, and a beacon laser source is added next to it, so thatthe FSM can steer its beam within the detector’s FOV. This FSM is also connected tothe PMC via a mirror driver. The PMC can steer it independently and in parallel tothe main control loop, and this way generate a disturbance “for itself” to control.The mounted optics in the final testbed can be seen in Figure 4.6, and a diagramvisualizing the interfaces between all the components in Figure 4.7.

Figure 4.6: Final version of the laboratory testbed, including the NODE pointing system, thePCENTER measurement setup, and a setup for simulating the beacon drift.

56 EXPERIMENT

Figure 4.7: A block diagram of interfaces between each component in the final testbed.

4.4.1 Representative Disturbance

In order to make the pointing control verification representative of on-orbit oper-ation, an expected body pointing error dataset is generated for the external FSMto “play”. This will ensure that the beacon drift on the FPA will be as close aspossible to what is expected on orbit during the spacecraft ground-tracking slewmaneuver, which the bus will be performing during each overpass.

The dataset generation is based on information available from the bus ADCSspecification, which includes statistical information about the pointing accuracy,stability, and potential pointing offset due to payload misalignment with regardsto the ADCS reference frame. A summary of these parameters is given in Table4.3.

A MATLAB script is written to generate a body pointing error waveform follow-

4.4. DISTURBANCE SIMULATION 57

Table 4.3: Parameters used for ADCS pointing error data generation.

Parameter SpecificationPointing accuracy ± 0.15 deg (3σ)Pointing stability ± 0.0225 deg/s (3σ)Worst-case pointing bias ± 1 deg

ing these specifications. In the first step, random errors with a normal distributionare generated using the MATLAB randn function. One dataset is generated forboth the X and Y axis, with the same amplitude and standard deviation, so thatboth axes are exercised equally. These sets are then scaled to make the standarddeviation of the total error correspond to the ADCS pointing accuracy (i.e. 0.05deg 1σ). A constant offset is also added to each axis, so that the total mean er-ror equals the worst-case pointing offset of 1 deg. The samples are then spacedin time in a way that the magnitude RMS rate agrees with the pointing stabilityspecification. Finally, the samples for each axis are splined together with a smallsampling period, and exported to a file as a waveform that can be played by thePMC. The waveforms are generated for a duration of 10 minutes, which roughlycorresponds to a satellite overpass duration when in LEO.

An example of a waveform resulting from the script is visualized and analyzedin Figure 4.8. It can be seen that the resulting error distribution precisely followsthe assumptions given by the bus ADCS specification. The expected planar drift ofthe beacon signal over one OGS overpass as seen by the payload detector is alsoshown in a trace plot in Figure 4.8.

58 EXPERIMENT

0 1 2 3 4 5 6 7 8 9 10 11

Time, t (min)

0.85

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intin

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0.85 0.9 0.95 1 1.05 1.1 1.15

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| (deg)

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Y E

rro

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2D ADCS Error Trace

Figure 4.8: On the top, a magnitude plot of the ADCS body pointing error as a functionof time. The bottom left plot shows the error distribution, which conforms with the ADCSspecification. On the bottom right, a 2D trace of the waveform is shown, as is expected to beseen by the NODE beacon detector over one OGS overpass.

4.5. POINTING CONTROL VERIFICATION 59

4.5 Pointing Control Verification

The last and the most important experiment focused on verification of the wholefine pointing chain, and analyzing its performance with regards to pointing preci-sion. The testbed was configured for two end-to-end tests, one for each fine point-ing mode, i.e. either running with open-loop or closed-loop FSM control. Thetests included FSM calibration, beacon acquisition, beacon tracking, and pointingcontrol for the duration of one overpass. The test procedure was as follows:

1. The FSM calibration algorithm is executed with the calibration laser on.(Manual step)

2. The laser is switched off and the system begins beacon acquisition.(Automatic step)

3. The FSM in the disturbance generation setup starts playback of the bodypointing error waveform to simulate body pointing drift.(Manual step)

4. The beacon laser is turned on.(Manual step)

5. The system acquires the beacon and begins pointing control.(Automatic step)

6. After the body pointing simulation concludes, the pointing chain is stopped.(Manual step)

During the actual tracking and control phase, the PMC was configured to collectall samples of the beacon and the feedback signal for accuracy evaluation. Thisprocess is detailed for each mode in the following sections.

4.5.1 Open-Loop Test

In the open-loop FSM pointing mode, the feedback laser is not utilized in the chainafter the calibration phase. As is summarized in Figure 3.17, the FSM steering isperformed using the calibrated affine map immediately after a new sample of thebeacon signal is obtained. However, for the sake of the pointing accuracy test, wekeep the laser turned on, although it is not being used to drive the FSM. Instead,the samples are only kept in memory, and then saved into a file together with thebeacon samples when the pointing chain finishes. Processing this file then enablesevaluation of the pointing error after the test.

60 EXPERIMENT

0 2 4 6 8 10

Time, t (min)

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To

tal E

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| (

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-600 -300 0 300 600

X Error, X

( rad)

-600

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300

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Y E

rror,

Y

(ra

d)

Error Scatter

Error

Requirement

Figure 4.9: Time and scatter plots of fine pointing error obtained during the open-loop point-ing test. The NODE pointing requirement is also visualized in the scatter plot as a red circle.

-300 -200 -100

X Error, X

( rad)

-100 0 100

Y Error, Y

( rad)

100 150 200 250 300

Total Error, | | ( rad)

Occurrence

PDF Fit

Figure 4.10: Statistical analysis of the error distribution. The orthogonal component his-tograms are fit to a Gaussian and the magnitude histogram is fit to a Rician distribution.

Figure 4.9 shows the magnitude of the pointing error during the test, both asa function of time, and also component wise as an aperture-plane scatter plot.It can be seen that the error has a constant offset (i.e. a steady state error ispresent), which is expected due to the nature of this control mode. The scatterplot illustrates that this error is, however, well within the required accuracy region.


The red circle on the scatter plot corresponds to the± 0.65 mrad pointing accuracyrequirement, which was defined earlier in Chapter 2.

To obtain reasonable accuracy metrics from the measurements, the error his-tograms are fit to probability distribution functions (PDFs), from which the meanand the standard deviation are calculated. The data is fit in MATLAB using thefitdist function, which is visualized in Figure 4.10. The orthogonal componentsof the error vector are fit to a Gaussian distribution, while the magnitude his-togram is fit to a Rician distribution. The Rician distribution is appropriate sincethe magnitude is a norm of bivariate normally distributed components which havenon-zero mean. A summary of the calculated statistical parameters is given in Ta-ble 4.4.

Table 4.4: Pointing accuracy metrics from the open-loop pointing test.

Mean (µrad) σ (µrad)θX -193.5 22.0θY 36.9 17.7

|θ| 197.5 23.8

4.5.2 Closed-Loop Test

The second test followed the same procedure, but was configured to utilize the cal-ibration signal to drive the FSM with the designed closed-loop integral controller.Both the beacon and the feedback signals were sampled with the double-windowtracking technique, and the FSM was steered after each update of the feedbacksignal (following the concept in Figure 3.17). Using this configuration, the controlloop was running at an update rate of roughly 30 Hz.

The same body pointing disturbance dataset was used, so that a representativecomparison between the two modes could be obtained. The measured fine point-ing errors are summarized in Figure 4.11. We can observe that the controller isperforming as is expected, since the error converges to zero for both axes. Simi-larly as in the previous case, we derive the pointing accuracy metrics by analysisof the error histograms. In this case, we fit the magnitude histogram using theRayleigh distribution, as both of the components have nearly zero mean normaldistributions. The obtained statistical values are summarized in Table 4.5.

62 EXPERIMENT

0 2 4 6 8 10

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Tota

l E

rror,

|| (

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( rad)

-600

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300

600

Y E

rro

r,

Y (

rad

)

Error Scatter

Error

Requirement

Figure 4.11: Time and scatter plots of fine pointing error obtained during the closed-looppointing test.

-100 0 100

X Error, X

( rad)

-100 0 100

Y Error, Y

( rad)

0 20 40 60 80 100

Total Error, | | ( rad)

Occurrence

PDF Fit

Figure 4.12: Statistical analysis of the error distribution. The orthogonal component his-tograms are fit to a Gaussian and the magnitude histogram is fit to a Rayleigh distribution.

4.5.3 Discussion

The performed hardware-in-the-loop pointing control tests were an important partof the fine pointing system verification process. We have shown that the fine point-ing stage is able to successfully reject a representative body pointing disturbance


Table 4.5: Pointing accuracy metrics from the closed-loop pointing test.

Mean (µrad) σ (µrad)θX 0.09 15.6θY -0.31 16.4

|θ| 20.0 10.5

that is expected by the payload on orbit. The analysis shows that under laboratoryconditions, both of the pointing modes can meet the pointing requirement withsignificant margin.

The results of the open-loop FSM pointing confirm that a steady state error isinevitable in this mode, as a certain constant bias can be seen in both axes. This ismainly determined by the uncertain regions in the calibrated feedback mapping,which mostly depend on the FSM repeatability and non-linearity. It can be seenthat especially the X axis error had a high mean value of nearly 200 µrad, whichis around double the calibration algorithm RMSE. Thus, it is likely that the FSMwas positioned around a higher uncertainty peak in the feedback map.

The closed-loop FSM control results show significant pointing precision improve-ments due to rejection of the steady state errors. Both orthogonal error compo-nents have a nearly zero mean and a standard deviation of roughly 16 µrad. Thetotal error has a mean magnitude of 20 µrad and a standard deviation of approx-imately 10 µrad. These errors were traced down primarily to two sources. Thefirst one is the lag between the beacon and the feedback signal samples. With acontrol frequency of 30 Hz and a body pointing error rate of up to 0.0225 deg/s,this can lead to fine pointing errors of up to 13 µrad, just due to the delays. Thesecond one is the readout noise of the beacon detector, which leads to noise insignal centroiding. This noise was measured to be a roughly 0.05 px RMSE, whichcorresponds to 5 µrad. Ultimately, if the system is calibrated well for misalignmentand the ~50 µrad 3σ pointing accuracy is reached during operation on orbit, itwould result in essentially negligible pointing losses (-0.005 dB) with the currentdownlink beam divergence. This would be a good motivation to decrease thebeam divergence and aim for higher downlink rates in future iterations of NODE.

To improve the pointing accuracy even further, a few hardware and softwareupgrades are feasible. Some form of a non-linear feedback mapping with moredegrees of freedom could be estimated for the case of open-loop pointing. Thismight help reduce the mapping uncertainty that exists due to small non-linearitiesin the system. The closed-loop control errors could be reduced for example byusing a higher frame-rate detector, which would reduce the sample lag, and couldalso utilize frame averaging to mitigate centroiding noise.

CHAPTER 5

Conclusion

In this chapter, we conclude the thesis with a short summary of the addressedtopics and the achieved results. Specific contributions are highlighted, and futurework related to the pointing subsystem is discussed.

5.1 Thesis Summary

The rapid increase of small satellites on orbit is accompanied by higher downlinkdemand, which becomes problematic with traditional RF technology. Limited pay-load size, weight, power, and strict regulations lead to communications systemswith low rates that are bottlenecks for many proposed data-intensive missions.The Nanosatellite Optical Downlink Experiment (NODE) developed at MIT is aim-ing to demonstrate the feasibility of using laser communications to achieve highdownlink rates within a highly constrained platform of a 3U CubeSat.

In this thesis, we focus on the fine laser pointing system of NODE, which is re-quired to improve the downlink beam pointing precision due to spacecraft bodypointing errors. The primary objective of this work was to build a flight-like lab-oratory testbed of the system, develop pointing algorithms for its hardware, andverify its functionality and pointing precision in an end-to-end hardware-in-the-loop test. A specific area of focus was the development of a technique to improvethe pointing precision and robustness by utilizing an internal calibration laser.

Chapter 1 motivates the need of a scalable high rate communications solution forsmall satellites. Several recently proposed highly data-intensive missions are pre-sented. The problem of significantly increasing downlink rates on small satellitesusing standard RF technology is investigated. Next, the benefits and challenges oflaser communications are explored.

Chapter 2 provides more research background on the area of fine laser pointingand NODE itself. Two recent space laser communications demonstrations are in-

65

66 CONCLUSION

vestigated. Their pointing systems are analyzed in detail, and their key parametersare compared to the NODE design parameters. Afterwards, the NODE system-levelarchitecture is presented, and its pointing accuracy requirement is derived to be±0.65 mrad.

Chapter 3 presents and analyzes the optics and the fine pointing mechanismused in NODE in detail. A beam steering solution based on a ground beacondetector and a fast steering mirror (FSM) is described. Since the miniature FSMsdo not have feedback sensors, the benefit of utilizing an internal calibration laseris emphasized. An approach on the design of an open-loop as well as a closed-loop FSM controller is presented. Next, algorithms for signal sampling on thedetector are outlined, followed by a technique to automatically calibrate the FSMfor precise pointing by estimating a mapping between its input and the detector’sreference frame. Lastly, the whole designed control process chain is summarized.

Chapter 4 describes the laboratory testbed assembly and the carried out ex-periments. Results show that the designed FSM calibration algorithm enableson-demand open-loop pointing of the FSM with a root mean square error of 98µrad with regards the beacon detector’s reference frame. The algorithm takes lessthen 10 seconds to finish and can be ran on orbit before an overpass if needed.A method that enables the measurement and software compensation of optome-chanical misalignment in the system is also presented. Ultimately, an approachon verification of the whole pointing control chain is described. A representa-tive spacecraft body pointing disturbance is simulated in the laboratory with thefine pointing control loop engaged. Both open-loop and closed-loop FSM controlmodes are analyzed for overall pointing accuracy. Experimental results show thatboth modes fulfill the pointing accuracy requirement with significant margin, andthat in the closed-loop control mode, 1σ error as low as 16 µrad can be achievedfor each axis. The mean of the fine pointing error magnitude was measured to be198 µrad and 20 µrad for the open-loop and closed-loop modes respectively. Themain sources of error were traced down to uncertainty in the feedback map foropen-loop control, and sample lag and centroiding noise for closed-loop control.

5.2 Contributions

Specific contributions of this work are highlighted below:

• Assembly and alignment of a laboratory testbed with flight hardware, whichcan be used for fine laser pointing experiments.

• Development of a novel detector sampling technique, which allows trackingof two laser signals independently without mutual interference.

5.3. FUTURE WORK 67

• Development of a robust on-orbit FSM calibration algorithm that increasesthe optical feedback accuracy.

• Design of a laboratory setup and method to measure and compensate foroptomechanical misalignment in the system.

• Implementation of all the algorithms in the fine pointing control chain onthe payload microcontroller in C++.

• Experimental analysis of the designed FSM calibration algorithm with re-gards to re-visit precision of the feedback map.

• Verification of the pointing system in an end-to-end test, which simulatedspacecraft body pointing disturbance over one OGS overpass.

• Statistical analysis of the achievable pointing accuracy in both open-loop andclosed-loop FSM pointing modes under the expected disturbance.

5.3 Future Work

Further areas of work needed on the fine pointing system for the path to flight:

• The testbed utilizes a FSM driver by Mirrorcle Technologies, but a customcompact board is being fabricated for the NODE payload. The embeddedsoftware has to be updated to command the FSM through the new driver,which is interfaced to an FPGA that controls the laser transmitter.

• A more rigorous solution on adapting the beacon detector’s exposure withregards to the received beacon power has to be implemented. A simplecontrol loop that adapts the exposure based on the signal intensity could bedesigned, with appropriate logic for detection of beacon loss.

• While the pixel grouping algorithm can reject individual “hot pixels” (dueto radiation damage), a more robust solution should be implemented to de-crease risk. The beacon camera offers calibration functionality to detect de-fective pixels, which should be researched as a possible improvement.

• A solution to monitor and debug the fine pointing system as part of thepayload telemetry/telecommand has to be implemented. Information fromthe pointing chain should be fused with other telemetry generated by thepayload microcontroller for analysis on ground.

68 CONCLUSION

• The pointing precision and ability to compensate optomechanical misalign-ment should be tested in thermal vacuum (TVAC) conditions for better un-derstanding of the expected performance on orbit.

Areas that may be beneficial for further study:

• Experimental analysis of the benefit of estimating a non-linear feedbackmapping with more degrees of freedom between the calibration signal cen-troid and the FSM input.

• Analysis of the benefit of a more advanced controller design with regardsto error rejection. An adaptive Linear-Quadratic-Integral (LQI) controllercould be investigated as a replacement for the calibrated feedback mappingand the simple integral controller.

• Testing if a high frame-rate detector would lead to rejection of errors due tosample lag and centroiding noise by utilizing frame averaging.

APPENDIX A

Alternative Feedback Designwith a Retro-Reflector

Because of the problems with the determination of PCENTER due to potential op-tomechanical misalignments, another alternative design solution was simultane-ously researched to tackle the issue with the optical pointing feedback. One plau-sible idea is to use a retro-reflector next to the dichroic mirror instead of a regularmirror. This would result in a case where the rays are not inverted at the detector,but would have the same angles of incidence as at the aperture. Consequently, foroptimal pointing, the spots would not need to mirror each other on the detector,but would copy each other’s position, as is visualized in Figure A.1.

Figure A.1: Ray geometry with a retro-reflector-based feedback.

69

70 REFERENCES

This solves the potential misalignment issue completely, as the retro-reflectorwill not bias the feedback signal, unlike a misaligned mirror would. However,it also means that the spots will always be sampled at the same point on theFPA, which will load to slight interference of the feedback signal, as discussed inSection 3.4.3. Moreover, retro-reflector prisms are bigger in volume, therefore asignificant redesign of the optomechanical payload structure would be necessary.Ultimately, it was decided to pursue the original design with a regular mirror, andcome up with a solution to compensate potential misalignment in software, whichwas discussed in Section 4.3.

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